Question

hich equation represents the circle described?

The radius is 2 units.
The center is the same as the center of a circle whose equation is x2 + y2 – 8x – 6y + 24 = 0.
(x + 4)2 + (y + 3)2 = 2
(x – 4)2 + (y – 3)2 = 2
(x – 4)2 + (y – 3)2 = 2²
(x + 4)2 + (y + 3)2 =

Answer 1

First find the center of x^2 + y^2 − 8x − 6y + 24 = 0 by completing the square:

(x^2 − 8x) + (y^2 − 6y) + 24 = 0
(x − 4)^2 − 16 + (y − 3)^2 − 9 + 24 = 0
⇒ (x − 4)^2 + (y − 3)^2 = 1

So the center is (4, 3). With radius 2 the equation is

(x − 4)^2 + (y − 3)^2 = 2^2 = 4,

which corresponds to the choice (x − 4)^2 + (y − 3)^2 = 2².