Question

If the center of a circle is (-5, -8) and contains the point (16, 68) what is the equation ?

Answer 1

`(x+5)^2+(y+8)^2=6217`

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

1) Plug the center of the circle into the equation

Center: (-5,-8)

`(x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-(-8))^2=r^2\\(x+5)^2+(y+8)^2=r^2`

2) Determine r²

Plug in the given point (16,68)

`(x+5)^2+(y+8)^2=r^2\\(16+5)^2+(68+8)^2=r^2\\(21)^2+(76)^2=r^2\\441+5776=r^2\\6217=r^2`

Therefore, r² is equal to 6217. Plug this back into
`(x+5)^2+(y+8)^2=r^2`:

`(x+5)^2+(y+8)^2=6217`

I hope this helps!