Question

Find the center and radius of the circle with equation (x – 7)2 + (y – 5)2 = 4.

Answer 1

Center: (7,5)

Radius: 2

Explanation:

A circle is defined as a set of points in a plane that are all of equal distance from the center. This distance from the center is called the radius. The equation of a circle in standard form is
`(x-h)^(2) + (y-k)^(2) = r^(2)` , where r represents the radius and
`(h,k)` represents the center.

Since the equation given in the problem is already in standard form, we can easily find the values that make up
`(h,k)`. We find that h = 7, and k = 5, so the center of the circle is (7,5). Since r² is equal to 4, we can calculate the square root to get a radius of r = 2.