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To find the points outside the circle

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by gmattesttaker2 » Sun Jan 19, 2014 6:09 pm
Hello,

Can you please assist with this?

Which of the following points lies outside
circle x^2 + y^2 = 25?

(A) (4, 3)
(B) (-4, -3)
(C) (9, 6)
(D) (2, 2)
(E) (2, 4)

OA: C

Thanks a lot,
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by ganeshrkamath » Sun Jan 19, 2014 9:00 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this?

Which of the following points lies outside
circle x^2 + y^2 = 25?

(A) (4, 3)
(B) (-4, -3)
(C) (9, 6)
(D) (2, 2)
(E) (2, 4)

OA: C

Thanks a lot,
Sri
The general equation for a circle with center (A,B) and radius r is:
(x-A)^2 + (y-B)^2 = r^2

Comparing this with the given equation, we get:
(A,B) = (0,0) and r = 5

The maximum value of x or y dimension is +/- 5.

The point (9,6) is clearly outside this limit.

Choose C

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by theCodeToGMAT » Sun Jan 19, 2014 10:23 pm
x^2 + y^2 = 25
the equation can be re-written as:
(x-0)^2 + (y-0)^2 = (5)^2
Here,
radius = 5
origin = (0,0)
Maximum magnitude of x & y points = 5

So, [spoiler]{C}[/spoiler]
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by GMATGuruNY » Mon Jan 20, 2014 4:41 am
gmattesttaker2 wrote:Hello,

Can you please assist with this?

Which of the following points lies outside
circle x^2 + y^2 = 25?

(A) (4, 3)
(B) (-4, -3)
(C) (9, 6)
(D) (2, 2)
(E) (2, 4)

OA: C

Thanks a lot,
Sri
x² + y² = r² is the equation of a circle that is centered at the origin and has a radius of r.
Thus:
x² + y² = 25 is the equation of a circle that is centered at the origin and has a radius of 5.
Since r=5, any point that is more than 5 places from the origin will be OUTSIDE the circle.
Since answer choice C -- (9.6) -- is more than 5 places from the origin, this point lies outside the circle.

The correct answer choice is C.
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by [email protected] » Mon Jan 20, 2014 3:42 pm
Hi Sri,

Each of the other explanations in this thread has focused on the "math" (solving that the radius of the circle = 5). Here's another way to look at the "math" though:

Since we're asked which of the points is "outside" the circle, and we're given an equation to work with, then the points "inside" the circle can be "plugged in" to the equation and will be <= 25.

ANY co-ordinate that, when plugged in, is > 25 would be outside the circle.

A: 4^2 + 3^2 = 25
B: (-4)^2 + (-3)^2 = 25
C: 9^2 + 6^2 = 117
D: 2^2 + 2^2 = 8
E: 2^2 + 4^2 = 20

The only answer that is > 25 is C

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