# What will be the equation of a circle with a center at (–3, –5) and a radius of 6 units?

**Solution:**

Given, center coordinates = (-3, -5) and radius = 6 units.

Using the standard equation of the circle, which is :

(x - h)^{2} + (y - k)^{2} = r^{2} , where:

h = x coordinate of the center

k = y coordinate of the center

Thus on substituting the value of h, k, and r in the standard equation, we get:

(x + 3)^{2} + (y + 5)^{2} = 6^{2}

⇒^{ }(x + 3)^{2} + (y + 5)^{2} = 36

Thus the equation of the circle, can be given as ^{ }(x + 3)^{2} + (y + 5)^{2} = 36.

⇒ x^{2} + y^{2} + 6x +10y = 36 - 9 -25

⇒ x^{2} + y^{2} + 6x +10y =2

## What will be the equation of a circle with a center at (–3, –5) and a radius of 6 units?

**Summary:**

The equation of the circle, can be given as ^{ }(x + 3)^{2} + (y + 5)^{2} = 36 or x^{2} + y^{2} + 6x +10y=2

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