Question

Which equation represents a circle with a center at (2, –8) and a radius of 11?

Answer 1

the equation of a circle is defined by: (x - h)² + (y - k)² = r² where
(h,k) represents the center of your circle and r = the radius

So (x - 2)² + (y + 8)² = 121 is your equation

Answer 2

The equation of circle is
`x^2+y^2-4x+16y-61=0`

Explanation:

Given : A circle with a center at (2, –8) and a radius of 11.

To find : Which equation represents a circle?

Solution :

The general equation of the circle is

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

Where, (h,k)=(2,-8) is the center and r is the radius r=11.

Substitute the value in the formula,

`(x-2)^2+(y-(-8))^2=11^2`

`x^2-4x+4+y^2+16y+64=121`

`x^2+y^2-4x+16y+60=121`

`x^2+y^2-4x+16y-61=0`

Therefore, The equation of circle is
`x^2+y^2-4x+16y-61=0`