How do you write the equation of a circle with the center (8,7) and radius r=6?

1 Answer
Mar 24, 2016

Answer:

The equation is
#x^2+y^2-16x-14y+77=0#

Explanation:

As a circle is a point that moves so that its distance from a given point (called center) is always same (called radius), we should first calculate the distance of a point #(x,y)# from the center at #(8,7)# and that should be #6#, as radius is given to be #6#.

Hence #sqrt((x-8)^2+(y-7)^2)=6#

Now squaring both sides, we get

#(x-8)^2+(y-7)^2=36# or

#x^2-16x+64+y^2-14y+49=36# or

#x^2+y^2-16x-14y+64+49-36=0# or

#x^2+y^2-16x-14y+77=0#

graph{x^2+y^2-16x-14y+77=0 [-20, 20, -5, 15]}