Find an equation of the circle that has a center (3,-2) and passes through (4,4)

Answer 1

The equation for any general circle is

(x-h)² + (y-k)² = r²

So you have the center (h,k) = (3, -2)

And it passes through the point (4,4).

So from the center to any point on the circle is the radius. We can find the radius by finding the distance between the center (3, -2) and the point on the circle (4,4).

d = sqrt( (4-3)² + (4-(-2))²) = sqrt(1 + 36) = √37 = our radius

So the equation of the circle is:

(x-3)² + (y+2)² =(√37)²

or

(x-3)² + (y+2)² = 37