Question

The circle below is centered at the point (5,3) and has a radius of length 4. What is it’s equation

Answer 1

`{x}^(2) + {y}^(2) - 10x - 6y + 18 = 0`

Answer 2

`(x-5)^2 + (y-3)^2= 16` is the equation of a circle

Explanation:

The circle below is centered at the point (5,3) and has a radius of length 4

To find the center form of equation, we use formula

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

where (h,k) is the center and 'r' is the radius of the circle

given center is (5,3)

h=5 and k =3

radius r= 4, plug in all the values in the equation

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

`(x-5)^2 + (y-3)^2= 4^2`

`(x-5)^2 + (y-3)^2= 16` is the equation of a circle