Question

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

Answer 1

$\huge{\bold{\red{Heya!!!}}}$

$\bold{\blue{Here\:is\:your\: answer\: }}$


first let us rearrange the equation of parabola in the desired form
Now, y2 + 4y  = - 4x - 2 
y2 + 4y + 4 = - 4x - 2 + 4  (adding 4 on both sides to have perfect square)
 (y+2)2 = -4 (x -1/2)
Resembling (y-k)2 = - 4a (x-h) with vertex (h,k) and length of latus rectum 4a
This is equivalent ot Y2 = -4a X (by shifting the origin to (h,k)
-ve sign indicates that parabola is facing left ward
In this directrix X = a
By comparison ours with this we have
a = 1
Directrix is (x-1/2) = 1
Or x = 3/2