Write the equation of the circle with center (-1, 9) and containing the point (2, 5)

The standard equation of the circle is:

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center point and r is the radius.

Here we need to find the radius which will just be the distance from the center to the point on the circle given.

The distance can be found by the "distance formula" which is really just a result of the Pythagorean Theorem.

d^2=(x2-x1)^2+(y2-y1)^2  (notice how it looks just like the circle equation :P)

Here d is the radius so d^2 is the radius squared too, anyway.

d^2=(2--1)^2+(5-9)^2

d^2=9+16

d^2=25 so

r^2=25

And since we are given that the center is (-1,9) we can write out our circle equation...

(x+1)^2+(y-9)^2=25