Question

The center of the circle is (-4,5). the circle passes through (-4,3). what is it’s radius?

Answer 1

-The radius:

`r=2`

-The result for the equation of a circle (if needed):

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

Explanation:

-The equation of a circle is:

`(x - h)^2 +(y-k)^2=r^2` where the center is
`(h,k)`, the point
`(x,y)` and the radius is
`r`,

-Next, use the center (-4,5) and the point (-4,3) for this equation:

`(-4+4)^2 +(3-5)^2=r^2`

-Then, you solve the equation:

`(-4+4)^2 +(3-5)^2=r^2`

`0 +(-2)^2=r^2`

`4 = r^2`

`√(4) =√(r^2)`

`2 = r`

Therefore, the result for the radius is 2.

-The result for the equation of a circle:

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