Question

What is the equation of the circle with: center (5, 7) and point on the circle: (-2, 8)

Answer 1

`(x-5)^2+(y-7)^2=50`

Explanation:

Hi there!

Equation of a circle:
`(x-h)^2+(y-k)^2=r^2` where the circle is centered at
`(h,k)` and r is the radius

Plug in the center (5,7)

`(x-5)^2+(y-7)^2=r^2`

Plug in the given point (-2,8) to solve for r²

`(-2-5)^2+(8-7)^2=r^2\\(-7)^2+(1)^2=r^2\\49+1=r^2\\50=r^2`

Therefore, r² is equal to 50. Plug this back into
`(x-5)^2+(y-7)^2=r^2`

`(x-5)^2+(y-7)^2=50`

I hope this helps!