A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle?
(x + 2)² + (y - 5)² = 16
(x + 2)² + (y + 5)² = 16
(x + 2)² + (y - 5)² = 4
(x - 2)² + (y + 5)² = 4

Solution:

Given: Center of the circle = (-2 ,5) and radius = 4 units.

We know 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 given circle, (α, β) is the center of the given circle and r is the radius of the given circle.

Now, put the values of the center and the radius in the equation (1)

We get,

⇒ (x - (-2))² +(y - 5 )² = 4²

⇒ (x + 2)² + (y - 5)² = 4²

Now solving the equation using the following identities

(x + y)² = x² + y² + 2xy

(x - y)² = x² + y² - 2xy

⇒ x² + 2² + 2.2.x + y² + 5² - 2.5.y = 4²

⇒ x² + 4 + 4x + y² + 25 - 10y = 16

⇒ x² + y² + 4x - 10y = 16 - 25 - 4

⇒ x² + y² + 4x - 10y = -13

⇒ x² + y² + 4x - 10y + 13 = 0

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A circle has its center at (-2, 5) and a radius of 4 units. What is the equation of the circle?

Summary:

A circle having its center as (-2, 5) and radius = 4 units will have its equation as (x + 2)² + (y - 5)² = 4².