Question

The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is (x + 21)^2 + (y + 19)^2 = 849. what is the centerpoint of circle and radius? please help me

Answer 1

Equation of a circle is given by (x - a)^2 + (y - b)^2 = r^2; where (a, b) is the center of the circle and r is the radius.

For the given circle: (x + 21)^2 + (y + 19)^2 = 849
(x - (-21))^2 + (y - (-19))^2 = (√849)^2

a = -21, b = -19 and r = √849
Therefore, the centerpoint of the circle is (-21, -19) and the radius is √849