Identify the type of graph.
-$6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$
A) The graph is the point (-1, 3).
B) The graph is a circle with center (1, -3).
C) The equation has no graph.
D) The graph is an ellipse with center (1, -3).

Question

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + Cy^2 + Dx + Ey + F = 0$, where $A$ and $C$ are both positive and not equal, indicating an ellipse. Completing the square for both $x$ and $y$ terms and dividing the whole equation by the coefficient of $x^2$ and $y^2$ (which are equal in this case) would give an equation in the standard form of an ellipse. The center of the ellipse can be found by transforming the equation into its standard form, which reveals the center to be at (1, -3).

Identify the Type of Graph 6x2−12x+3y2+18y−21=06 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 06x2−12x+3y2+18y−21=0

Identify the Type of Graph $6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$