Question

What is the center and radius of the circle with the equation `5(x+5)^2+5(y+2)^2=60`?

Answer 1

centre`" "(-5,-2)`

radius`" "2sqrt3`

Explanation:

standard eqn. of circle centre `" "(a,b)" "`radius`" "r`

`(x-a)^2+(y-b)^"=r^2`

so`" "5(x+5)^2+5(y+2)^2=60`

divide through by `" "5`

`" "(x+5)^2+(y+2)^2=12`

comparing with the standard qn.

centre`" "(-5,-2)`

radius`" "sqrt12=2sqrt3`

Answer 2

The center of the circle is `(-5,-2)` and the radius `=2sqrt3`

Explanation:

We compare this equation to the standard equation of the circle, center `(a,b)` and radius `r`

`(x-a)^2+(y-b)^2=r^2`

Our equation is

`5(x+5)^2+5(y+2)^2=60`

Dividing by `5`

`(x+5)^2+(y+2)^2=12`

`(x+5)^2+(y+2)^2=(2sqrt3)^2`

So the center of the circle is `(-5,-2)` and the radius `=2sqrt3`

graph{(x+5)^2+(y+2)^2=12 [-11.25, 11.25, -5.63, 5.62]}