Question

Find an equation of the circle that has center (-4, 1) and passes through (3, -5)

Answer 1

The general equation for a circle with center (a,b) and squared radius k is

$(x-a)^2 + (y-b)^2 = k$

Here we have

$(x- - 4)^2 + (y -1)^2 = k$

and the constant is fixed by substituting in the point we know (x,y)=(3,-5)

$(x + 4)^2 + (y-1)^2 = (3+4)^2 + (-5-1)^2 = 85$

Answer:

$(x + 4)^2 + (y-1)^2 = 85$