Question

Which equation represents a circle with a center at (-4,9) and a diameter of 10 units?

Answer 1

`(x+4)^2 + (y-9)^2 = 25`

Explanation:

To write the equation of a circle, use the formula
`(x-h)^2+(y-k)^2 = r^2` where the center of the circle is (h, k).

This means the equation is
`(x--4)^2 + (y-9)^2 = r^2\\\(x+4)^2 + (y-9)^2 = r^2`.

Find the radius r by dividing the diameter of 10 in 2. The radius is 5.

So the equation of the circle is
`(x+4)^2 + (y-9)^2 = 25`