The equation of the directrix of the parabola y2+4y+4x+2=0 is

Question

The equation of the directrix of the parabola y2+4y+4x+2=0 is (A)  -1  (B)  x=1  (C)  x=-3/2  (D)  x=3/2

Tardigrade Admin · Accepted Answer

Given equation can be rewritten as (y+2)2=-4( x-(1/2) ) ⇒ s Y2=-4X, where Y=y+2 and X=x-(1/2) . The equation of directrix is X=1 . ∴ x-(1/2)=1 ⇒ x=(3/2)

Q. The equation of the directrix of the parabola $y^{2} + 4 y + 4 x + 2 = 0$ is

$- 1$

$x = 1$

$x = - 3/2$

$x = 3/2$

Given equation can be rewritten as $(y + 2)^{2} = - 4 (x - \frac{1}{2})$
$\Rightarrow$ s $Y^{2} = - 4 X,$
where $Y = y + 2$ and $X = x - \frac{1}{2}$ .
The equation of directrix is $X = 1$ .
$∴$ $x - \frac{1}{2} = 1 \Rightarrow x = \frac{3}{2}$

Q. The equation of the directrix of the parabola y2+4y+4x+2=0 is

−1

x=1

x=−3/2

x=3/2