Question

Write the equation of the circle centered at (4,-1) that passes through (13,8).

Answer 1

`(x-4)^2+(y+1)^2=162`

Explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

`(x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\`

Hence, the equation of the circle that meets these criteria is
`(x-4)^2+(y+1)^2=162`