what is the equation of the circle with center (2,-5) that passes through the pooint (-2,20)
The general equation for a circle with center (a,b) and radius r is:
(x-a)^2 + (y-b)^2 = r^2
In this case, the center is (2,-5) and the point (-2,20) is given as lying on the circle. We can use these two pieces of information to solve for the radius, r:
(-2-2)^2 + (20+5)^2 = r^2
16 + 625 = r^2
641 = r^2
r = sqrt(641)
Now we can plug in the center and radius to get the equation of the circle:
(x-2)^2 + (y+5)^2 = 641