Question

Write the equation of the circle centered at ( − 8 , − 4 ) that passes through ( 15 ,− 8 )?

Answer 1

`(x+8)^2+(y+4)^2=545`

Explanation:

Your circle has the equation of `(x-x_c)^2 + (y-y_c)^2 = r^2`
where `x_c` is the value of x of the center, and `y_c` is the value of y of the center and r is the radius. So here where the center is at (-8, -4), you circle is `(x+8)^2+(y+4)^2=r^2`
Time to find the radius (r):
Your circle passes through (15,-8) which means that `(15+8)^2+(-8+4)^2=r^2`
`=> 23^2+(-4)^2=r^2`
`=> r^2=525`
So finally, your circle is: `(x+8)^2+(y+4)^2=545`