Last visit was: 18 Nov 2025, 19:53 It is currently 18 Nov 2025, 19:53
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
TheUltimateWinner
avatar
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,489
Kudos: 2,387
 [19]
In the xy plane, a circle is drawn with the center at (3, -2). The cir 06 Jul 2020, 09:49
1
Kudos
Add Kudos
18
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

53% (02:50) correct 47% (02:21) wrong based on 104 sessions

History

Date
Time
Result
Not Attempted Yet
In the xy-plane, a circle is drawn with the center at (3, -2). The circle intersects the x-axis at two points that are 2√14 apart. What is the distance between the points of intersection of the circle and the y-axis?

A) 4
B) 5
C) 6
D) 7
E) 8
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 18 Nov 2025
Posts: 4,145
Own Kudos:
10,983
 [8]
Given Kudos: 99
Expert
Expert reply
Posts: 4,145
Kudos: 10,983
 [8]
In the xy plane, a circle is drawn with the center at (3, -2). The cir 16 Jul 2020, 14:07
7
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
TheUltimateWinner
In the xy-plane, a circle is drawn with the center at (3, -2). The circle intersects the x-axis at two points that are 2√14 apart. What is the distance between the points of intersection of the circle and the y-axis?

A) 4
B) 5
C) 6
D) 7
E) 8
Show more

The question is abusing language, so it's inherently confusing. What is the source? Normally when we ask for "the distance between (something) and (something else)", we want the distance between the first thing and the second. But here, when the question asks for "the distance between the points of intersection of the circle and the y-axis", they do not mean to ask for the distance between "the points of intersection of the circle" and "the y-axis". They mean to ask for the distance between the two points where the circle meets the y-axis, or in other words, between the two y-intercepts of the circle.

There are faster ways to solve this problem if you use math that goes beyond the scope of the GMAT. I'll limit myself only to GMAT math -- we know the x-axis meets the circle at two points that are 2√14 apart. By symmetry, one of these points will be √14 to the left of the center of the circle, and the other will be √14 to the right. So the two x-intercepts of the circle must be at (3 - √14, 0) and (3 + √14, 0). These are points on the circle, and we know the center of the circle is at (3, -2), so using either point we can find the radius of the circle using Pythagoras (which is the same thing as the distance formula in coordinate geometry) :

r^2 = (3 + √14 - 3)^2 + (0 - 2)^2
r^2 = (√14)^2 + (-2)^2
r^2 = 18
r = 3√2

If (0, b) is a y-intercept of the circle, we know it must be 3√2 away from the circle's center (3, -2), so again using the distance formula:

(3 - 0)^2 + (-2 - b)^2 = (3√2)^2
9 + (b + 2)^2 = 18
(b + 2)^2 = 9

and if (b+2)^2 = 9, then b+2 is equal either to 3 or to -3, and b is equal either to 1 or -5. So the two y-intercepts are at (0, 1) and (0, -5) which are a distance of 6 apart.
General Discussion
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 06 Nov 2025
Posts: 1,849
Own Kudos:
8,236
 [1]
Given Kudos: 707
Location: India
Posts: 1,849
Kudos: 8,236
 [1]
In the xy plane, a circle is drawn with the center at (3, -2). The cir 06 Jul 2020, 11:58
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Attachment:
Untitled.png
Untitled.png [ 5.45 KiB | Viewed 6049 times ]
AO = √14 -3
OB = √14 +3

Suppose CD = 2y

CO = y-2
OD = y+2

\((y-2)(y+2) = [√14 -3 ]* [√14 +3 ]\)

\(y^2-4 = 5\)

y=3

2y =6
User avatar
summerbummer
User avatar
Joined: 16 Jul 2020
Last visit: 22 Sep 2025
Posts: 47
Own Kudos:
17
Given Kudos: 137
Location: India
GMAT 1: 520 Q39 V23
GMAT 2: 600 Q42 V30
GMAT 2: 600 Q42 V30
Posts: 47
Kudos: 17
In the xy plane, a circle is drawn with the center at (3, -2). The cir 16 Jul 2020, 12:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nick1816
Attachment:
Untitled.png
AO = √14 -3
OB = √14 +3

Suppose CD = 2y

CO = y-2
OD = y+2

\((y-2)(y+2) = [√14 -3 ]* [√14 +3 ]\)

\(y^2-4 = 5\)

y=3



2y =6
Show more


how did you get ao and ob
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 17 Jul 2025
Posts: 3,086
Own Kudos:
3,102
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,086
Kudos: 3,102
In the xy plane, a circle is drawn with the center at (3, -2). The cir 16 Jul 2020, 12:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel IanStewart even i am confused regarding the question, can you explain this with a better POE.
User avatar
nick1816
User avatar
Retired Moderator
Joined: 19 Oct 2018
Last visit: 06 Nov 2025
Posts: 1,849
Own Kudos:
8,236
 [2]
Given Kudos: 707
Location: India
Posts: 1,849
Kudos: 8,236
 [2]
In the xy plane, a circle is drawn with the center at (3, -2). The cir 16 Jul 2020, 13:04
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
summerbummer
Attachment:
Untitled.png
Untitled.png [ 8.86 KiB | Viewed 5673 times ]

Perpendicular from the center to the chord bisects the chord.

Hence, AX = XB = √14

OX = (3-0) = 3

AO = AX - OX = √14 - 3

OB = XB + OX = √14 + 3

If you still have any doubt, you can ask.
avatar
TheUltimateWinner
avatar
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,489
Kudos: 2,387
In the xy plane, a circle is drawn with the center at (3, -2). The cir 04 Aug 2020, 13:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TheUltimateWinner
In the xy-plane, a circle is drawn with the center at (3, -2). The circle intersects the x-axis at two points that are 2√14 apart. What is the distance between the points of intersection of the circle and the y-axis?

A) 4
B) 5
C) 6
D) 7
E) 8
Show more
Is there anyone to share easiest way, please? I really appreciate your help.
User avatar
Nups1324
User avatar
Joined: 05 Jan 2020
Last visit: 12 Sep 2023
Posts: 105
Own Kudos:
64
Given Kudos: 353
Posts: 105
Kudos: 64
In the xy plane, a circle is drawn with the center at (3, -2). The cir 05 Aug 2020, 06:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TheUltimateWinner
In the xy-plane, a circle is drawn with the center at (3, -2). The circle intersects the x-axis at two points that are 2√14 apart. What is the distance between the points of intersection of the circle and the y-axis?

A) 4
B) 5
C) 6
D) 7
E) 8
Show more



Hi,

I got the correct answer by using some logic of my own. I'd like to share the same.

The question says distance between the "Points" of intersection and Y Axis.

Please use the image shared by nick1816 as a reference towards my explanation.

The center has to be (3,-2) so imagine a center at (3,-2).
Now try to draw a circle from that point. Remember the circle intersects at 2 points on the X Axis which are 2√14 apart. But that can be anywhere. So assume any radius for this circle.

For example 6 units.
So go 6 units right from 3 on the X Axis. [3 is the original center so imagine using a geometry compass from (3,-2) and take 6 units and draw a circle. You'll intersect X Axis at 9]

This is one point of intersection.

Now go the same 6 units left from 3 on the X axis. You'll get -3 on the negative side of X Axis.

This is second point of intersection.


Now the distance between these two and the Y Axis.

Distance from 9 (Positive X Axis) to Y Axis = 9
Distance from Y Axis to -3 (Negative X Axis) = -3

9 + (-3) = 6

Take any number as radius and do the above calculation, you'll always get 6 as the answer.


This is purely based on my logic. I might be wrong.


My heart says this is correct but my brain says something is wrong or missing. :lol:

Therefore, I humbly request Bunuel, chetan2u, nick1816, yashikaaggarwal to check my explanation and let me know how close am I to the correct logic.

It will be great if any of you or any of your expert friends gave us some insights.

DON'T RELY ON THIS UNLESS ANY ONE OF THE EXPERTS CONFIRM IT.

Please don't mind the shape of my circle in the picture that I've attached.

Lastly, I'm sorry if my logic has hurt any math enthusiast or math lover due to its potential loopholes.


Thank you.

Posted from my mobile device
Attachments

20200805_190011.jpg
20200805_190011.jpg [ 2.67 MiB | Viewed 5227 times ]

User avatar
Fdambro294
User avatar
Joined: 10 Jul 2019
Last visit: 20 Aug 2025
Posts: 1,350
Own Kudos:
741
Given Kudos: 1,656
Posts: 1,350
Kudos: 741
In the xy plane, a circle is drawn with the center at (3, -2). The cir 30 Oct 2021, 18:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
As IanStewart thankfully pointed out, the question is asking for the distance between the Y-Intercepts (at least that is what the credited response of 6 gives us).


Because a circle is a collection of equidistant points from the center, the circle will come up and intersect one point on the X Axis (point A) and come around counterclockwise and intersect another point on the X Axis (point B) —— such that every point on the circumference is equidistant from the center.

Thus, Point A and Point B will each be a distance of R = radius from the center of the Circle, point O at (3 , -2)


Rather than use the circle, we can use the Rules and Symmetry of an Isosceles triangle when an altitude is dropped from the apex vertex.


Connect 2 radii from the Center O to points A and B.


The distance between the two X intercepts is 2 * sqrt(14) and this will be the Base of the triangle = Side AB

OA = OB = radius = R ———> are the other 2 equal sides of the Isosceles Triangle


Rule: the height originating from the apex vertex O at (3 , -2) and drawn perpendicular to base side AB, as a line of symmetry, will also be the Median of the isosceles triangle and Bisect Side AB.

Call the point at which this height bisects side AB —- point D

Since the distance between the 2 X intercepts (points A and B) is given as 2 * sqrt(14)

AD = sqrt(14) = DB

The length from center (3 , -2) to point D on the X Axis is given by the vertical distance from the line Y = 0 to the line Y = -2 ————> 2 units

We can then use the Pythagorean Theorem to find the radius of the circle (which is the two equal sides, OA and OB, of the Isosceles triangle)

(AD)^2 + (2)^2 = (R)^2

(Sqrt(14))^2 + (2)^2 = (R)^2

18 = (R)^2


Lastly, we can set up the equation for a Circle and find the two Y intercepts.

The equation of this circle, with center at point O (3 , -2), is given by:

(x - 3)^2 + (y + 2)^2 = 18


The Y intercepts will occur at the point where the X coordinate is 0:

(0 - 3)^2 + (y + 2)^2 = 18

9 + (y)^2 + 4y + 4 = 18

(y)^2 + 4y - 5 = 0

(y + 5) (y - 1) = 0


The Y intercepts - the points at which the circle will intersect the Y Axis - will occur at:

(0 , -5)

And

(0 , +1)

This is a vertical distance of 6 units

Answer: 6

yashikaaggarwal
Bunuel IanStewart even i am confused regarding the question, can you explain this with a better POE.
Show more

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,589
Own Kudos:
1,079
Posts: 38,589
Kudos: 1,079
In the xy plane, a circle is drawn with the center at (3, -2). The cir 03 Mar 2025, 11:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts