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 = r² --- (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 = 3²

⇒ (x + 2)² +(y - 3)² = 3²

Expanding the above equation by using the algberaic identities

(x + y)² = x² + y² + 2xy

(x - y)² = x² + y² - 2xy

⇒ x² + 2² + 4x + y² + 3² - 2.3.y = 3²

⇒ x² + 4 + 4x + y² + 9 - 6y = 9

⇒ x² + y² + 4x - 6y + 9 + 4 - 9 = 0

⇒ x² + y² + 4x - 6y + 4 = 0

Summary:

The equation of the circle with center (-2,3) and radius = 3 units will be x² + y² + 4x - 6y + 4 = 0.

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