Identify the type of graph.
-$$2 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 0$$
A) The graph is a circle with center $( 1 , - 3 )$.
B) The graph is an ellipse with center $( 1 , - 3 )$.
C) The graph is the point $( - 1,3 )$.
D) The equation has no graph.

Question

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + Cy^2 + Dx + Ey + F = 0$, where $A$ and $C$ are coefficients of $x^2$ and $y^2$ respectively, and both are positive but not equal, indicating an ellipse. The center of the ellipse can be found by completing the square for $x$ and $y$ terms, which results in a center at $(1, -3)$.

Identify the Type of Graph 2x2−4x+5y2+30y−43=02 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 02x2−4x+5y2+30y−43=0

Identify the Type of Graph $2 x ^ { 2 } - 4 x + 5 y ^ { 2 } + 30 y - 43 = 0$