What is the equation of a circle of radius 6 units centered

What is the equation of a circle of radius 6 units centered at (3, 2)?

A. x2 + y2 + 6x – 4y = 23
B. x2 + y2 - 6x + 4y = 23
C. x2 + y2 + 6x + 4y = 23
D. x2 + y2 - 6x – 4y = - 23
E. x2 + y2 - 6x – 4y = 23

The equation will be :
\((x-3)^2+(y-2)^2=6^2\)
If you simplify this, you'll get (e)

Posted from GMAT ToolKit

Just did backsolving by picking one point in circle such as (9, 2)

Option C where all summed is not true, so it must be options with subtracting.

Chose E and it is correct


E

Answer E by simplifying circle equation: (x−3)^2+(y−2)^2=6^2

Hi,

chetan2u, Bunuel, VeritasKarishma, Gladiator59, generis

Is this type of question is part of GMAT as have never seen such question in official book or in the books of Manhattan.

Coordinate geometry is a part of GMAT as per the conventional wisdom, but I guess it would be unlikely to see such a direct formula based question on the real exam. But you never know

But having said all that, it is still not too different from questions which do show up on the real exam - viz. coordinate geometry with lines. So it would do no harm to try and understand how the problem can be tackled. You can find all you need about this problem here.

If you know that the equation of a circle centered at (a,b) with a radius of r is -
\((x-a)^2 + (y-b)^2 = r^2\)

This question then becomes a piece of cake.

we surely are expecting middle terms in the binary squares to have negative coefficients - and hence all except D & E are eliminated at first sight. Now, the constant terms of the two binomial expansions will add up to 13 (3^2 + 2^2) and hence the RHS will be 36 - 13 or 23. Hence Option (E) is correct.

Thanks a ton Gladiator59

It seems very unlikely to me that a question like this would ever show up on the GMAT. The question is designed to reward test takers who memorize specialized formulas, and the GMAT is not a test of how many formulas you can memorize, so it's just not in the style of an authentic question. It's not completely impossible that such a question could appear, because even without knowing a formula, a test taker can find other ways to answer (e.g. just noticing (9,2) must be on the circle, and so x=9 and y=2 must satisfy the circle's equation, is all you need), but it seems extremely unlikely to me.

When it comes to circles in coordinate geometry, the only equation I've ever needed to answer official GMAT questions is this one:

x^2 + y^2 = r^2

which is the equation for a circle centred at (0, 0), with radius r. The GMAT can test that particular coordinate geometry equation because you can see fairly easily with a diagram that every point (x, y) on that circle needs to satisfy the Pythagorean Theorem (where |x| and |y| are the short sides, and the radius r is the hypotenuse), so the equation for that circle must be precisely the Pythagorean Theorem, x^2 + y^2 = r^2, which every test taker needs to know.

Posted from my mobile device