Question

A circle is centered at (−4, −6) and has a radius of 3. Which of the following is the equation for this circle?

(x + 4)2 + (y + 6)2 = 3
(x − 4)2 + (y − 6)2 = 9
(x − 4)2 + (y − 6)2 = 3
(x + 4)2 + (y + 6)2 = 9

Answer 1

(x + 4)2 + (y + 6)2 = 9 is the equation of this circle.

Explanation:

The standard equation of a circle with center (h, k) and radius r is

(x-h)^2 + (y-k)^2 = r^2. Please use " ^ " for exponentiation.

We can immediately discard the 1st and 3rd answers, since the radius squared is 3^2, or 9.

Comparing

(x - h)^2 + (y-k)^2 = r^2 to

(x + 4)2 + (y + 6)2 = 9 shows that h = -4 and k = -6, as well as r = 3.

Therefore, (x + 4)2 + (y + 6)2 = 9 is the equation of this circle.

Answer 2

(x+4)^2 +(y+6)^2 = 9

Explanation:

The equation for a circle is given by

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

(x- -4)^2 + (y--6)^2 = 3^2

(x+4)^2 +(y+6)^2 = 9