Question

Find an equation of the circle that has center (-6,5) and passes through (2,6)

Answer 1

`(x+6)^2+(y-5)^2=65`

Explanation:

Plug center into the equation of a circle

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

`(x-(-6))^2+(y-5)^2=r^2`

`(x+6)^2+(y-5)^2=r^2`

Determine r²

`(2+6)^2+(6-5)^2=r^2`

`8^2+1^2=r^2`

`64+1=r^2`

`65=r^2`

Final equation

`(x+6)^2+(y-5)^2=65`