white the equation

Question

Write the equation of the circle centered at  that passes through 

Answer 1

Equation of a circle with center (h,k) and radius r is (x-h)^2+(y-k)^2=r^2

In your case (h,k)=(5,-6) so your equation so far looks like (x-5)^2+(y+6)^2=r^2.

Now you have to figure it out the radius r. To do this you take point (-5,8) which is on the circle and plugs in the equation to find r

(-5-5)^2+(8+6)^2=r^2

100+196=r^2

296=r^2

So your circle equation is

(x-5)^2+(y+6)^2=296

Answer 2

An equation of the circle with center (h,k) and radius r is (x-h)² + (y-k)² = r².

So, we have (x-5)² + (y+6)² = r²

Since the point (-5,8) is on the circle, (-5-5)² + (8+6)² = r²

r² = 296

Equation of circle: (x-5)² + (y+6)² = 296

Answer 3

Use the distance formula for (5, -6) to (-5, 8).

This is the radius, r

(x - 5)² + (y + 6)² = r²