How do you write the standard from of the equation of the circle given center (-2, 4) and radius 7?

1 Answer
Sep 14, 2016

Answer:

#(x+2)^2 +(y-4)^2 =49#

Explanation:

The standard or general form of a circle is
#(x-h)^2 +(y-k)^2 = r^2#

where #(h,k)# is the center of the circle and #r# is the radius.

In this problem, #h=-2#, #k=4# and #r=7#

Plugging these values into the equation gives:

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

#(x+2)^2 +(y-4)^2 =49#

Some teachers refer to the "standard form" as the equation resulting from squaring the binomials and gathering all terms on one side. This is uncommon, but here it is.

#(x+2)(x+2) +(y-4)(y-4)=49#

#x^2 +4x +4 +y^2 -8y +16=49#

Rearranging and combining the constant terms gives

#x^2 +y^2+4x-8y-29=0#