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`