What is the center and radius of a circle with equation y^2-4*y+x^2-8*x+4 =0
The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2.
The equation of the circle in the problem is y^2-4*y+x^2-8*x+4 =0. Let us rewrite this in the form given earlier so that the center and radius can be determined.
=> y^2 - 4y + 4 + x^2 - 8x + 16 = -4 + 4 + 16
=> (y - 2)^2 + (x - 4)^2 = 16 = 4^2
The center of the given circle is (4, 2) and the radius of the circle is 4 units.