Question

Which of the following is the equation of a circle with center (5 -2) and a radius of 3

Answer 1

`(x-5)^2+(y+2)^2=9`

Explanation:

The information that we know about the circle is the following:

center of the circle: (5, -2)

radius:
`r=3`

We use the general form for the equation of a circle whose center is at the point
`(h,k)` :

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

In this case since the center of our circle is at (5, -2), we conclude that:

`h=5`

and

`k=-2`

so we substitute this values, along with the value for the radius:

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

simplifying the expression we get the equation of the circle:

`(x-5)^2+(y+2)^2=9`