How do you find the center (h,k) and radius r of the circle with the given equation #x^2+y^2-18x+18y=-137#?

1 Answer
Jan 20, 2016

The centre is #(9,-9)# and the radius is #5#

Explanation:

The equation needs to be rearranged into the form #(x-h)^2 + (y-k)^2 = r^2#

First reorder the expression to group the #x# and #y# terms
#x^2 - 18x +y^2 +18y = -137#

Each group then needs to be expressed as a square by completing the squares

#(x-9)^2 -9^2 + (y+9)^2 -9^2 = -137#
#(x-9)^2 +(y+9)^2 = -137 +81 +81 = 25#

The circle is then #(x-9)^2 + (y+9)^2 = 25#

The centre is therefore #(9,-9)# and the radius is #5#