Question

A circle is centered at (-4, 6) and has a radius of 9. What is the equation of the circle?

Answer 1

Solution given:

centre (h,k)=(-4,6)

radius [r]=9

we have

equation of a circle

(x-h)²+(y-k)²=r²

(x+4)²+(y-6)²=9²

(x+4)²+(y-6)²=81 is a required equation

Answer 2

C

Explanation:

The standard equation for a circle is given by:

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

Where (h, k) is the center of the circle and r is the radius.

We want to find the equation of a circle that is centered on (-4, 6) and has a radius of 9 units.

Therefore, (h, k) = (-4, 6).

And r = 9.

By substitution:

`(x-(-4))^2+(y-(6))^2=(9)^2`

Simplify. Hence, our equation is:

`(x+4)^2+(y-6)^2=81`

Our answer is C.