Identify the conic as a circle, parabola, ellipse, or hyperbola. $$2 x ^ { 2 } = 8 x + 3 \left( y ^ { 2 } - 8 y \right) + 46$$
A) circle
B) hyperbola
C) parabola
D) ellipse
E) none of the above

Question

Quizplus · Accepted Answer

The given equation can be rewritten in the standard form of a conic section by completing the square for both x and y terms. The presence of both $x^2$ and $y^2$ terms with opposite signs (after moving the 8x to the other side and factoring out the coefficients) indicates a hyperbola.

Identify the Conic as a Circle, Parabola, Ellipse, or Hyperbola 2x2=8x+3(y2−8y)+462 x ^ { 2 } = 8 x + 3 \left( y ^ { 2 } - 8 y \right) + 462x2=8x+3(y2−8y)+46

Identify the Conic as a Circle, Parabola, Ellipse, or Hyperbola $2 x ^ { 2 } = 8 x + 3 \left( y ^ { 2 } - 8 y \right) + 46$