Write the standard form the equation for the circle that passes through the points (-9,-16),(-9,32), and (22,15)? then identify the center and radius?

1 Answer
Jun 25, 2018

#(x+9)^2=(y-8)^2=576#
Center: #(-9,8)#
Radius: #24#

Explanation:

We need to know the center and radius of the circle before we can write the equation. We only need to focus on #(-9,-16)# and #(-9,32)# because the other coordinate will confuse us and give us unnecessary work.
First, notice how we have the same x-value and two y-values in our equation. That means we have a diameter! As you know, a diameter is two times the radius:

#16+32=2r#
#48=2r#
#24=r#

Next, let's find the center. The center is the midpoint between our two coordinates, so let's just subtract our radius from #(-9,32)#:

#(-9,32-24) = (-9,8)#

All we have to do next is plug our values into the standard formula for a circle:

#(x-h)^2+(y-k)^2=r^2#
#(x-(-9))^2+(y-8)^2=24^2#
#(x+9)^2=(y-8)^2=576#