A circle has a center located at the point (-2, 5) and a radius of 6 units. What is the eq… — ACT

A circle has a center located at the point $(-2, 5)$ and a radius of $6$ units. What is the equation of this circle in the $(x, y)$ coordinate plane?

$(x + 2)^2 + (y - 5)^2 = 36$ Answer
B
$(x - 2)^2 + (y + 5)^2 = 36$
C
$(x + 2)^2 + (y - 5)^2 = 6$
D
$(x - 2)^2 + (y - 5)^2 = 36$
E
$(x - 2)^2 + (y + 5)^2 = 6$

The equation of the circle is

(x + 2)^2 + (y - 5)^2 = 36

The correct equation is found by substituting the center

(-2, 5)

and radius

6

into the standard equation

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

. This yields

(x - (-2))^2 + (y - 5)^2 = 6^2

, which simplifies to

(x + 2)^2 + (y - 5)^2 = 36

Identify the standard form equation of a circle.

The standard equation is

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

, where

(h, k)

represents the center coordinates and

r

represents the radius.

This general equation is the mathematical template for representing any circle in a coordinate plane.

Substitute the given values for the center

(-2, 5)

and the radius

6

into the equation.

(x - (-2))^2 + (y - 5)^2 = 6^2

Plugging in

h = -2

k = 5

, and

r = 6

customizes the general formula to this specific circle.

Simplify the signs of the terms and calculate the squared radius.

(x + 2)^2 + (y - 5)^2 = 36

Subtracting

-2

simplifies to adding

2

, and squaring the radius of

6

yields

36

Standard equation of a circle given its center and radius

Question