# What are the coordinates of the center of the circle #x^2 + y^2 -8x -10y -8=0#?

##### 1 Answer

May 17, 2016

#### Explanation:

Complete the squares for

#0 = x^2+y^2-8x-10y-8#

#= color(blue)(x^2-8x+16)+color(green)(y^2-10y+25)-49#

#= color(blue)((x-4)^2)+color(green)((y-5)^2)-7^2#

Add

#(x-4)^2+(y-5)^2 = 7^2#

This is in the form of the standard equation of a circle:

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

with center

graph{((x-4)^2+(y-5)^2-7^2)((x-4)^2+(y-5)^2-0.06)=0 [-16.67, 23.33, -5.2, 14.8]}