How do you write the equation for a circle with center at (-5, 6) and diameter = 16?

1 Answer
May 11, 2016

Answer:

#(x+5)^2+(y-6)^2=64#

Explanation:

The general equation for a circle with center #(a,b)# and radius #r# is
#color(white)("XXX")(x-a)^2+(y-b)^2=r^2#

We are told the center #(a,b)=(-5,6)#
and that the diameter #=16#
which implies the radius is #r=8#

So we have
#color(white)("XXX")(x-(-5))^2+(y-6)^2=8^2#
or
#color(white)("XXX")(x+5)^2+(y-6)^2=64#

Here is the graph for #(x+5)^2+(y-6)^2=64#
graph{(x+5)^2+(y-6)^2=64 [-20.35, 15.68, -3.46, 14.56]}