Question

A circle is centered at (-4, 6) and has a radius of 9. What is the equation of the circle? Question 3 options: (x+4)2+(y−6)2=18 (x+4)2+(y−6)2=81 (x−4)2+(y+6)2=18 (x−4)2+(y+6)2=81

Answer 1

(x+4)² + (y-6)² = 81

Explanation:

General equation of a circle : (x-h)² + (y-k)² = r²

where (h,k) is at center and r = radius

Here we are given that the circle has a center at (-4,6) and a radius of 9

So we have (h,k) = (-4,6) so h = -4 and k = 6 and radius = 9 so r = 9

Plugging in values into general equation

Recall that the general equation of a circle is (x-h)² + (y-k)² = r²

we have h = -4 , k = 6 and r = 9

==> plug in values

doing so we acquire (x-(-4))² + (y-6)² = 9²

==> apply double negative sign rule

(x+4)² + (y-6)² = 9²

==> evaluate exponent

(x+4)² + (y-6)² = 81

And we are done!