Question

Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?

(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y – 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36

Answer 1

The equation of a circle is always the same:

`(x - h)^(2) + (y - k)^(2) = r^(2)`
where (h, k) is the center of a circle and r is its radius. So, we have:

`(x +3)^(2) + (y +5)^(2) = 36`
The answer is the last one.

Answer 2

Option D. (x + 3)² + (y + 5)² = 36

Explanation:

We have to find the equation of a circle given with a center at (-3, -5) and radius of 6.

Since the standard equation of a circle is

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

where (h, k) is the center and r is the radius.

Now we form an equation of a circle given with center (-3, -5) and radius = 6 units.

(x + 3)² + (y + 5)² = 6²

(x + 3)² + (y + 5)² = 36

Therefore Option D is the answer.