GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 22:31

### 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

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

# In the xy-plane, a circle C is drawn with center at (1, 2) and radius

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Feb 2017
Posts: 59
In the xy-plane, a circle C is drawn with center at (1, 2) and radius  [#permalink]

### Show Tags

05 Jan 2018, 09:53
3
5
00:00

Difficulty:

85% (hard)

Question Stats:

45% (02:33) correct 55% (02:25) wrong based on 44 sessions

### HideShow timer Statistics

In the xy-plane, a circle C is drawn with center at (1, 2) and radius equal to 5. Is line l a tangent to the circle C?

(1) Point A with coordinates (a, b) lies on line l such that a(a-2)+ b(b-4) ≤ 20.

(2) The x-intercept of line l is 10.

_________________
+1 Kudos if you find it helpful.
Senior Manager
Joined: 22 Feb 2018
Posts: 428
Re: In the xy-plane, a circle C is drawn with center at (1, 2) and radius  [#permalink]

### Show Tags

15 Mar 2018, 22:15
1
mandeey wrote:
In the xy-plane, a circle C is drawn with center at (1, 2) and radius equal to 5. Is line l a tangent to the circle C?

(1) Point A with coordinates (a, b) lies on line l such that a(a-2)+ b(b-4) ≤ 20.

(2) The x-intercept of line l is 10.

In the xy-plane, a circle C is drawn with center at (1, 2) and radius equal to 5
from this information , we can find out the equation of circle .
$$(x-1)^2 +(y-2)^2 = 5^2$$
Solving it , we get $$x^2 + 1 -2x +y^2 +4 - 4y = 25$$
$$x^2+y^2-2x-4y-20=0$$

Now we have to give yes/no answer to question: Is line l a tangent to the circle C?

Statement 1:Point A with coordinates (a, b) lies on line l such that a(a-2)+ b(b-4) ≤ 20.
Instead taking coordinate (a,b), we will cordinate as (x.y) in order to findout general equation.
We get $$x^2 +y^2 - 2x- 4y ≤ 20$$
Substracting 20 from both side,
$$x^2 +y^2 - 2x- 4y-20≤0$$
This implies that (x,y) or (a,b) according to statement 1 should lie on circumference of circle or inside it.
As Statement 1 gives us condition that point(a,b) of line l lies inside or on circumference of circle, it is insufficient for defining a particular line.

Statement 2: The x-intercept of line l is 10.
It means that line passes through point (10,0)
There can be infinite line passing through the point (10,0)
So this statement is also insufficient.

Combining Statement 1 and Statement 2 , Statemen1 gives condition for (a,b) on line l.
All Coordinate inside circle and on circumference will satisfy the condition.
There will be infinite number of line connecting point (a,b) and (10,0) , point as given by statement 2.
We do not have value of slope, in order to define a single line.
So Statement 1 and 2 together also are not sufficient.

I am adding a rough image , hope it can add some clarity to what i am trying to convey.

Please gives kudos and feedback if you like my explaination.
Attachments

IMG_20180316_103437535.jpg [ 2.06 MiB | Viewed 601 times ]

_________________
Good, good Let the kudos flow through you
Non-Human User
Joined: 09 Sep 2013
Posts: 11012
Re: In the xy-plane, a circle C is drawn with center at (1, 2) and radius  [#permalink]

### Show Tags

16 May 2019, 22:58
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 xy-plane, a circle C is drawn with center at (1, 2) and radius   [#permalink] 16 May 2019, 22:58
Display posts from previous: Sort by