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 = r² , where:

h = x coordinate of the center

k = y coordinate of the center

r = radius of the circle.

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

(x + 3)² + (y + 5)² = 6²

⇒ (x + 3)² + (y + 5)² = 36

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

⇒ x² + y² + 6x +10y = 36 - 9 -25

⇒ x² + y² + 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 x² + y² + 6x +10y=2