If the equation represents a hyperbola, find the center, foci, and asymptotes. If the equation represents an ellipse, find the center, vertices, and foci. If the equation represents a circle, find the center and radius. If the equation represents a parabola, find the focus and directrix.
-$$\mathrm { y } ^ { 2 } + 4 \mathrm { x } + 2 \mathrm { y } - 3 = 0$$
A) F: $\left( \frac { 3 } { 4 } , - 1 \right) ; \mathrm { D } : \mathrm { y } = \frac { 5 } { 4 }$
B) F: $( 0 , - 1 ) ;$ D: $x = 2$
C) $\mathrm { F } : ( 2,1 ) ; \mathrm { D } : \mathrm { y } = 0$
D) F: $( - 3,1 ) ;$ D: $\mathrm { y } = - 5$

Question

Quizplus · Accepted Answer

Completing the square, we get $$\left(y+1\right)^2 = -4x -4 +4 = -4\left(x+1\right)\implies \frac{\left(y+1\right)^2}{4} = -\left(x+1\right)$$
This is the equation of a horizontal parabola with focus at $(-1,-1)$ and directrix $x=2$.

If the Equation Represents a Hyperbola, Find the Center, Foci y2+4x+2y−3=0\mathrm { y } ^ { 2 } + 4 \mathrm { x } + 2 \mathrm { y } - 3 = 0y2+4x+2y−3=0

If the Equation Represents a Hyperbola, Find the Center, Foci $\mathrm { y } ^ { 2 } + 4 \mathrm { x } + 2 \mathrm { y } - 3 = 0$