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

Answer:

Option D. (x + 3)² + (y + 5)² = 36

Step-by-step 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.