Question

the directrix of this parabola

Answer 1

The equation of the parabola is

${y}^{2} + 4y + 4x + 2 = 0$
Now we will condense this into the general form.

${y}^{2} + 4y + 4 + 4x + 2 = 4 \\ {(y + 2)}^{2} = 2 - 4x \\ {(y + 2)}^{2} = - 4( - \frac{1}{2} + x)$
Now replace (y+2) by Y and (x - 0.5) by X.

${y}^{2} = - 4x$
So a = -1

As we know the equation of directrix is

X = -a
X = 1

Now replace X by (x - 0.5)

x - 0.5 = 1
x = 1.5

Hence the equation of directrix of given parabola is
$x = \frac{3}{2}$