It is currently 22 Jun 2017, 15:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the rectangular coordinate system, points (4, 0) and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39589
In the rectangular coordinate system, points (4, 0) and [#permalink]

### Show Tags

11 Nov 2009, 13:13
1
This post received
KUDOS
Expert's post
31
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

48% (01:46) correct 52% (00:50) wrong based on 793 sessions

### HideShow timer Statistics

In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?

(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above
[Reveal] Spoiler: OA

_________________
VP
Joined: 05 Mar 2008
Posts: 1469
Re: Maximum value of the radius [#permalink]

### Show Tags

11 Nov 2009, 15:08
2
This post received
KUDOS
Bunuel wrote:
In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the
maximum possible value of the radius of C ?

(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above

I'm getting E

It can be B, but the points mentioned can be a chord and that would make the radius larger. I'm getting other calculations but none are available or can't be determined.
Manager
Joined: 11 Sep 2009
Posts: 129
Re: Maximum value of the radius [#permalink]

### Show Tags

11 Nov 2009, 16:04
6
This post received
KUDOS
3
This post was
BOOKMARKED
The answer is E.

It takes 3 distinct points to define a circle. Only 2 are given here.

The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius is greater than 4. It does not give us an upper limit.
Senior Manager
Joined: 31 Aug 2009
Posts: 417
Location: Sydney, Australia
Re: Maximum value of the radius [#permalink]

### Show Tags

11 Nov 2009, 17:48
Agree with E.

Another way to look at it is that the two points, lets call them A and B, are equidistant to the centre of the circle, lets call that O. i.e. OA = OB
Hence the centre will lie on the Y axis (anywhere where x = 0).
So not enough information to determine.

Yet another way to look at it is:
Radius^2 = (Difference of X of O to A)^2 + (Difference of Y of O to A)^2
From the question stem we know that A is (4,0). Using the above logic we also know that the centre lies on x=0. Using B would yield the same result as we are after distance it will always end up being positive anyway.
This formula reduces to (4-0)^2 + (y-0)^2 = R^2
Depending on the value of y, the length of the radius will keep growing.
Senior Manager
Joined: 01 Mar 2009
Posts: 367
Location: PDX
Re: Maximum value of the radius [#permalink]

### Show Tags

11 Nov 2009, 20:42
Yep E , we need to know the origin to determine the radius and from the above information we cannot determine the origin.
_________________

In the land of the night, the chariot of the sun is drawn by the grateful dead

Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: Maximum value of the radius [#permalink]

### Show Tags

12 Nov 2009, 09:00
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.
_________________
Intern
Joined: 27 Aug 2010
Posts: 23
Re: Maximum value of the radius [#permalink]

### Show Tags

19 Sep 2010, 01:43
The question is more like a DS question. Rephrase it and you will get "If two points given are enough to define the maximum possible radius of the circle?" The answer is no, cause the radius could be as low as 4 if the points are at the maximum distance from the center and the line between them is the diameter or the radius could be infinitely large if the line between the points is the chord.
Manager
Joined: 23 Sep 2009
Posts: 146
Re: Maximum value of the radius [#permalink]

### Show Tags

04 Nov 2010, 15:28
You made me think a lot..But I arrived at (E) since the two points can be a chord too...
IMO is (E) for me too
_________________

Thanks,
VP

Intern
Joined: 02 Sep 2010
Posts: 48
WE 1: Business Development Manger
WE 2: Assistant Manager-Carbon Trading
WE 3: Manager-Carbon Trading
Re: Maximum value of the radius [#permalink]

### Show Tags

29 Nov 2010, 02:06
Bunuel wrote:
The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction.
So if the points were in Ist and 3rd quadrant we could have calculated the distance
Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: Maximum value of the radius [#permalink]

### Show Tags

29 Nov 2010, 02:22
Expert's post
3
This post was
BOOKMARKED
rite2deepti wrote:
Bunuel wrote:
The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction.
So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________
Intern
Joined: 06 Nov 2010
Posts: 23
Re: Maximum value of the radius [#permalink]

### Show Tags

06 Jan 2011, 16:33
if we join the line connecting the the points (-4,0) and (4,0) to the center of the circle say (0,y), radius will be maximum at the point where the area formed by the above triangle is min. The area will be 0 if the height is 0, which means the center is in the line connecting two pnts (-4,0) and (4,0). Isn't?
Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: Maximum value of the radius [#permalink]

### Show Tags

06 Jan 2011, 18:17
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
praveenvino wrote:
if we join the line connecting the the points (-4,0) and (4,0) to the center of the circle say (0,y), radius will be maximum at the point where the area formed by the above triangle is min. The area will be 0 if the height is 0, which means the center is in the line connecting two pnts (-4,0) and (4,0). Isn't?

The red part is not correct.

Again: The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

Check 2 possible circles:
Circle with min radius of 4 (equation x^2+y^2=4^2):
Attachment:

radius 4.gif [ 3.22 KiB | Viewed 19577 times ]

Circle with radius of 5 (equation x^2+(y-3)^2=5^2):
Attachment:

radius 5.gif [ 2.78 KiB | Viewed 19577 times ]

Generally circle passing through the points (4, 0) and (– 4, 0) will have an equation $$x^2+(y-a)^2=4^2+a^2$$ and will have a radius of $$r=\sqrt{4^2+a^2}$$. As you can see min radius will be for $$a=0$$, so $$r_{min}=4$$ and max radius is not limited at all (as $$a$$ can go to +infinity as well to -infinity).

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________
Intern
Joined: 02 Feb 2011
Posts: 11
Re: Maximum value of the radius [#permalink]

### Show Tags

27 Apr 2011, 00:42
[quote="Mongolia2HBS"]Only 2 points are given, so E.[/quo

suppose the question says that what is the maximum possible radius of the among the given choices then we can try out the highest choices and foind out whether the the given choice satisfies the pythagoras eqn. so that way D is best.
Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: Maximum value of the radius [#permalink]

### Show Tags

25 Apr 2012, 11:38
hm, maybe it is not an elegant method, but still...

we have two points - (4, 0) and (– 4, 0) . Also we know the formula -(x-a)^2+(y-b)^2=r^2

(4-a)^2+(0-b)^2=(-4-a)^2+(0-b)^2

(4-a)^2=(-4-a)^2
a=0

since we cant find b, we have no clue about the position of the center. So, no chances to find the
maximum possible value of the radius

hope my logic is ok. let me know, if I am wrong
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: Maximum value of the radius [#permalink]

### Show Tags

25 Apr 2012, 12:31
LalaB wrote:
hm, maybe it is not an elegant method, but still...

we have two points - (4, 0) and (– 4, 0) . Also we know the formula -(x-a)^2+(y-b)^2=r^2

(4-a)^2+(0-b)^2=(-4-a)^2+(0-b)^2

(4-a)^2=(-4-a)^2
a=0

since we cant find b, we have no clue about the position of the center. So, no chances to find the
maximum possible value of the radius

hope my logic is ok. let me know, if I am wrong

Here is how can you solve this question with that approach: in-the-rectangular-coordinate-system-points-4-0-and-86703.html#p847714
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: In the rectangular coordinate system, points (4, 0) and [#permalink]

### Show Tags

27 Jun 2013, 23:47
Expert's post
1
This post was
BOOKMARKED
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

_________________
MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4390
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
Re: In the rectangular coordinate system, points (4, 0) and [#permalink]

### Show Tags

28 Jun 2013, 04:57
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

The only thing we know is that Points A(4,0) and B(-4,0) are on circumference. But that does not necessarily mean that they are opposite ends of diameter.

If they are opposite ends of diameter, Radius will be 4, but if they are opposite ends of circle's smallest chord then Radius would be far more greater then the values mentioned in Options. Hence Choice E is correct.
_________________
Intern
Joined: 15 Jul 2012
Posts: 42
Re: Maximum value of the radius [#permalink]

### Show Tags

25 Oct 2013, 08:45
Bunuel wrote:
rite2deepti wrote:
Bunuel wrote:
The OA is E.

The only thing we can conclude from the question that center lies on the Y-axis. But it could be ANY point on it, hence we can not determine maximum value of r.

Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction.
So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.

Can you please explain on what basis it is concluded that centre lies on Y axis. Secondly which part in Gmat math book the concept is given, I have gone through the book but I didn't find it.
Third can you please explain what is the concept which clarifies minimum point to make a circle & maximum radius concept.
Please Help
Math Expert
Joined: 02 Sep 2009
Posts: 39589
Re: Maximum value of the radius [#permalink]

### Show Tags

25 Oct 2013, 08:54
anu1706 wrote:
Bunuel wrote:
rite2deepti wrote:
Can we also conclude that the points (4,0) and (-4,0) lie in first and 2nd quadrant so with that we cannot calculate the distance between two points ( which will be radius of circle ) ; because in order to calculate distance we need points in opposite direction.
So if the points were in Ist and 3rd quadrant we could have calculated the distance

I think you are a little bit confused here.

You CAN calculate the distance between any two points with given coordinates on a plane (no matter in which quadrants they are). For example the distance between two points (4,0) and (-4,0) is simply 8.

Generally the formula to calculate the distance between two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ is $$d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$$.

Next, the distance between (4,0) and (-4,0) won't necessarily be the DIAMETER of a circle. The minimum length of a diameter is indeed 8 (so min r=4) but as ANY point on the y-axis will be equidistant from the given points then any point on it can be the center of the circle thus the maximum length of the radius is not limited at all.

For more check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.

Can you please explain on what basis it is concluded that centre lies on Y axis. Secondly which part in Gmat math book the concept is given, I have gone through the book but I didn't find it.
Third can you please explain what is the concept which clarifies minimum point to make a circle & maximum radius concept.
Please Help

Please check here: in-the-rectangular-coordinate-system-points-4-0-and-86703.html#p847714
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15915
Re: In the rectangular coordinate system, points (4, 0) and [#permalink]

### Show Tags

23 Feb 2015, 12:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: In the rectangular coordinate system, points (4, 0) and   [#permalink] 23 Feb 2015, 12:18

Go to page    1   2    Next  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
9 In the rectangular coordinate system shown above, points O, P, and Q r 6 09 Apr 2017, 23:48
6 In a rectangular coordinate system, if a line passes through the point 4 03 May 2016, 00:49
15 In the rectangular coordinate system Point O has coordinates 11 15 Oct 2016, 22:09
8 In the rectangular coordinate system above, if point R (not 8 04 Jun 2017, 01:34
47 In a rectangular coordinate system, point A has coordinates 19 20 Aug 2016, 00:11
Display posts from previous: Sort by

# In the rectangular coordinate system, points (4, 0) and

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.