Identify the equation without completing the square.
-$$y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$$
A) parabola
B) ellipse
C) hyperbola
D) not a conic

Question

Quizplus · Accepted Answer

The given equation is of the form $Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$, where $A = -4$, $B = 0$, $C = 1$, and the coefficients of $x^2$ and $y^2$ have opposite signs ($-4$ and $1$, respectively). This indicates that the equation represents a hyperbola.

Identify the Equation Without Completing the Square y2−4x2+8x+4y+3=0y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0y2−4x2+8x+4y+3=0

Identify the Equation Without Completing the Square $y ^ { 2 } - 4 x ^ { 2 } + 8 x + 4 y + 3 = 0$