Which equation represents circle C?

The equation of the circle is

(x + 4)^2 + (y-1)^2 = 162

Step-by-step explanation:

Here, we want to give the correct equation of the circle.

The center of the circle is (-4,1)

Now the other parameter we need to show the equation of the circle is the radius of the circle and this can be obtained from the distance between the circle center and a point on the circumference.

We use the distance formula to calculate this.

So the distance we want to calculate is the distance between;

(-4,1) and (5,-8)

using the distance formula, we have

d = √(x2-x1)^2 + (y2-y1)^2

Substituting these values, we have;

d = √(5 + 4)^2 + (-8-1)^2

d = √(9^2 + 9^2)

d = √(162)

d = 9 √2 units

The formula for the equation of a circle is

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

where (h,k) are coordinates of the center which is (-4,1) in this question

The way of the circle is thus,

(x-(-4)^2 + (y-1)^2 = {9√(2)}^2

(x + 4)^2 + (y-1)^2 = 162