Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 6 x - 4 y - 12 = 0$$
A) no; the graph is the point $( 3,2 )$
B) yes
C) no; the graph is the point $( - 3 , - 2 )$
D) no; the graph is nonexistent

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the standard form of a circle's equation by completing the square for both x and y terms. Completing the square for $x^2 - 6x$ gives $(x-3)^2 - 9$, and for $y^2 - 4y$ gives $(y-2)^2 - 4$. Substituting these into the original equation and adding the constants to the other side gives $(x-3)^2 + (y-2)^2 = 25$, which is the equation of a circle centered at $(3, 2)$ with a radius of $5$.

Decide Whether or Not the Equation Has a Circle as Its