A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle?

Solution:

Given: Center of circle = (-1,2) 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 - (-1))² +(y - 2)² = 3²

⇒ (x + 1)² +(y - 2)² = 3²

Expanding the above equation by using the algberaic identities

(x + y)² = x² + y² + 2xy

(x - y)² = x² + y² - 2xy

⇒ x² + 1 + 2x + y² + 2² - 2.2.y = 3²

⇒ x² + 1 + 2x + y² + 4 - 4y = 9

⇒ x² + y² + 2x - 4y + 5 = 9

⇒ x² + y² + 2x - 4y = 9 - 5

⇒ x² + y² + 2x - 4y = 4

⇒ x² + y² + 2x - 4y - 4 = 0

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A circle has its center at (-1, 2) and a radius of 3 units. What is the equation of the circle?

Summary:

The equation of the circle with center (-1 , 2) and radius = 3 units will be x² + y² + 2x - 4y - 4 = 0.