Identify the type of graph.
$6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$
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

Identify the type of graph.
$6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$
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.

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. The center of the ellipse can be found by completing the square or transforming the equation into its standard form, which results in a center 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 $6 x ^ { 2 } - 12 x + 3 y ^ { 2 } + 18 y - 21 = 0$