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# 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

**Solution:**

We have standard form of the equation of circle whose centre at (h, k) and radius r as (x - h)^{2} + (y - k)^{2} = r^{2}

For example, if the equation of the circle is (x + 6)^{2} + (y - 5)^{2} = 64, then centre is (h, k) = (-6, 5) and radius r = 8

Given: Center (h, k) = (-3, -5) and radius r = 6

Substituting in the standard form of the equation of circle, we have

⇒ [x - (-3)]^{2} + [y - (-5)]^{2} = 6^{2}

⇒ (x + 3)^{2} + (y + 5)^{2} = 36

Therefore, the equation of circle is is (x + 3)^{2} + (y + 5)^{2} = 36.

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

**Summary: **

The equation that represents a circle with a center at (-3, -5) and a radius of 6 units is (x + 3)^{2} + (y + 5)^{2} = 36.

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