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A circle lies in an X-Y plane, with its center (1, -3)

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by jsl » Mon Oct 27, 2008 2:54 pm
A circle lies in an X-Y plane, with its center at (1, -3). If the distance between the X-intercepts of the circle is 8 units, what is the area of the circle?

9Pi
16Pi
25Pi
36Pi
64Pi

(dodgy question)... answer is 25Pi anyhow
Last edited by jsl on Tue Oct 28, 2008 4:41 am, edited 1 time in total.
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by earth@work » Mon Oct 27, 2008 3:54 pm
My answer is no where close to any of these options...dnt know where m getting wrong.
X-intercepts will be (5,0) and (-3,0)
dropping a perpendicular to x-axis, we get length of perpend = 3 coz (1.-3) is the center of the circle, the other side of triangle formed (on x-axis)=4 (=8/2)
Radius will be equal to the hypot. by applying pyth theorem
4^2+3^2=r^2
r=5
area=5x5x22/7=78 approx..
what m i doing wrong?
sorry cudn't help jsl.
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Re: A circle lies in an X-Y plane, with its center (1, -3)

by Ian Stewart » Mon Oct 27, 2008 3:55 pm
jsl wrote:A circle lies in an X-Y plane, with its center at (1, -3). If the distance between the X-intercepts of the circle is 8 units, what is the area of the circle?

9
16
25
36
64
None of the answer choices above is correct, clearly; there should be a Pi in each, presumably. I know the source of the question, and it's their mistake, not jsl's. In any case, if the x-intercepts are 8 apart, by symmetry they must be at (-3, 0) and (5, 0); that is, the x-co-ordinates of the intercepts must be 4 to the left and right of x=1, the x-co-ordinate of the centre of the circle. This is easier to see if you draw a diagram in the co-ordinate plane. Once you know these points on the circle, you can find that the distance to the centre is 5, so the circle's radius is 5. The area is then Pi*(5)^2 = 25*Pi.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by earth@work » Mon Oct 27, 2008 3:58 pm
thanks Ian... i was thinking that i m making some mistake in calculation or some error in my method
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Re: A circle lies in an X-Y plane, with its center (1, -3)

by gmat009 » Wed Oct 29, 2008 9:55 am
Ian Stewart wrote:
jsl wrote:A circle lies in an X-Y plane, with its center at (1, -3). If the distance between the X-intercepts of the circle is 8 units, what is the area of the circle?

9
16
25
36
64
None of the answer choices above is correct, clearly; there should be a Pi in each, presumably. I know the source of the question, and it's their mistake, not jsl's. In any case, if the x-intercepts are 8 apart, by symmetry they must be at (-3, 0) and (5, 0); that is, the x-co-ordinates of the intercepts must be 4 to the left and right of x=1, the x-co-ordinate of the centre of the circle. This is easier to see if you draw a diagram in the co-ordinate plane. Once you know these points on the circle, you can find that the distance to the centre is 5, so the circle's radius is 5. The area is then Pi*(5)^2 = 25*Pi.
Just one confusion Ian,
How we got this radius 5. IMO radius shud be 4.
Circle has centre at (1,-3) so radius shud be 4 instead of 5.
Plz. explain this.......
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Re: A circle lies in an X-Y plane, with its center (1, -3)

by Ian Stewart » Wed Oct 29, 2008 10:24 am
gmat009 wrote:
Ian Stewart wrote:
jsl wrote:A circle lies in an X-Y plane, with its center at (1, -3). If the distance between the X-intercepts of the circle is 8 units, what is the area of the circle?

9
16
25
36
64
None of the answer choices above is correct, clearly; there should be a Pi in each, presumably. I know the source of the question, and it's their mistake, not jsl's. In any case, if the x-intercepts are 8 apart, by symmetry they must be at (-3, 0) and (5, 0); that is, the x-co-ordinates of the intercepts must be 4 to the left and right of x=1, the x-co-ordinate of the centre of the circle. This is easier to see if you draw a diagram in the co-ordinate plane. Once you know these points on the circle, you can find that the distance to the centre is 5, so the circle's radius is 5. The area is then Pi*(5)^2 = 25*Pi.
Just one confusion Ian,
How we got this radius 5. IMO radius shud be 4.
Circle has centre at (1,-3) so radius shud be 4 instead of 5.
Plz. explain this.......
The center is at (1, -3), and (5,0) is a point on the circle, The distance from (1, -3) and (5,0) is 5, not 4 (draw the picture; you should get a 3-4-5 triangle).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by dmateer25 » Wed Oct 29, 2008 10:33 am
Hope this image helps
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Re: A circle lies in an X-Y plane, with its center (1, -3)

by gmat009 » Wed Oct 29, 2008 10:35 am
Ian Stewart wrote:
gmat009 wrote:
Ian Stewart wrote:
jsl wrote:A circle lies in an X-Y plane, with its center at (1, -3). If the distance between the X-intercepts of the circle is 8 units, what is the area of the circle?

9
16
25
36
64
None of the answer choices above is correct, clearly; there should be a Pi in each, presumably. I know the source of the question, and it's their mistake, not jsl's. In any case, if the x-intercepts are 8 apart, by symmetry they must be at (-3, 0) and (5, 0); that is, the x-co-ordinates of the intercepts must be 4 to the left and right of x=1, the x-co-ordinate of the centre of the circle. This is easier to see if you draw a diagram in the co-ordinate plane. Once you know these points on the circle, you can find that the distance to the centre is 5, so the circle's radius is 5. The area is then Pi*(5)^2 = 25*Pi.
Just one confusion Ian,
How we got this radius 5. IMO radius shud be 4.
Circle has centre at (1,-3) so radius shud be 4 instead of 5.
Plz. explain this.......
The center is at (1, -3), and (5,0) is a point on the circle, The distance from (1, -3) and (5,0) is 5, not 4 (draw the picture; you should get a 3-4-5 triangle).
Got it.....
Thanks Ian
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by gmat009 » Wed Oct 29, 2008 10:35 am
dmateer25 wrote:Hope this image helps
Great......
Thanks
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