Question

Find the equation of the circle with the center $(-2, 3)$ and radius $4$.

Answer 1

The equation of a circle with center (h, k) and radius r is given as

$(x - h)^2 + (y - k)^2 = r^2$

It is given that the center $(h, k) = (-2, 3)$ and radius (r) = 4.$$

Therefore, the equation of the circle is

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

$⇒ x^2 + 4x + 4 + y^2 - 6y + 9 = 16$

$⇒x^2 + y^2 + 4x - 6y - 3 = 0$ (Ans.)