# A circle has its center at (-2, 3) and a radius of 3 units. What is the equation of the circle?

**Solution: **

Given: Center of circle = (-2,3) and radius of the circle = 3 units

The general equation of a circle is given by (x - α)^{2} +(y - β)^{2} = r^{2} --- (1)

Where (x, y) is any point on the circle, (α, β) is the center of the given circle and 'r ' is the radius of the given circle.

Put the values in the equation 1

⇒ (x - (-2))^{2} +(y - 3)^{2} = 3^{2}

⇒ (x + 2)^{2} +(y - 3)^{2} = 3^{2}

Expanding the above equation by using the algberaic identities

(x + y)^{2} = x^{2} + y^{2} + 2xy

(x - y)^{2} = x^{2} + y^{2} - 2xy

⇒ x^{2} + 2^{2} + 4x + y^{2} + 3^{2} - 2.3.y = 3^{2}

⇒ x^{2} + 4 + 4x + y^{2} + 9 - 6y = 9

⇒ x^{2} + y^{2} + 4x - 6y + 9 + 4 - 9 = 0

⇒ x^{2} + y^{2} + 4x - 6y + 4 = 0

## A circle has its center at (-2, 3) and a radius of 3 units. What is the equation of the circle?

**Summary: **

The equation of the circle with center (-2,3) and radius = 3 units will be x^{2} + y^{2} + 4x - 6y + 4 = 0.