How do you write the equation of a circle with a center at (7, 3) and a diameter of 24?

1 Answer
Jan 20, 2016

Answer:

#(x-7)^2+(y-3)^2=12^2#

Explanation:

If the diameter is #24# then the radius is #r=24/2=12#

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

Substituting the given values for #(a,b)# and the calculated value for #r# gives
#color(white)("XXX")(x-7)^2+(y-3)^2=12^2#

Personally I think the equation should be left in this form. (it provides the maximum amount of information).

However if you need it "expanded":
#color(white)("XXX")x^2-14x+49+y^2-6y+9=144#

#color(white)("XXX")x^2+y^2-14x-6y=86#