Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$5 x ^ { 2 } + 5 y ^ { 2 } + 40 x - 30 y + 120 = 0$$
A) no; the graph is the point $( - 4,3 )$
B) no; the graph is the point $( 4 , - 3 )$
C) no; the graph is nonexistent
D) yes

Question

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + Ay^2 + Dx + Ey + F = 0$, where $A = 5$, $D = 40$, $E = -30$, and $F = 120$. Since the coefficients of $x^2$ and $y^2$ are equal and positive, and both $x^2$ and $y^2$ are present, the equation represents a circle.

Decide Whether or Not the Equation Has a Circle as Its