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

Correct Answer is : x=32 x=3/2x=23

Correct Answer is : x=32 x=3/2x=23

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MHTCET 26 Apr 2025 Shift 1 Paper

Question : 111 of 150

Marks: +1, -0

y^{2}+4 y+4 x+2=0

Solution:

Concept:

Recognize the standard form of a parabola and use its directrix formula.

Explanation:

Rewrite the given equation by completing the square:

y^{2}+4y+4x+2=0

\Rightarrow (y+2)^{2}-4+4x+2=0

\Rightarrow (y+2)^{2}=-4x+2

\Rightarrow (y+2)^{2}=-4\left(x-\frac{1}{2}\right)

This matches the form

Y^{2}=-4aX

, where

Y=y+2

X=x-\frac{1}{2}

, and

a=1

For this form, the directrix is

X=a

Therefore:

x-\frac{1}{2}=1

\Rightarrow x=\frac{3}{2}

Thus, the directrix is

x=\frac{3}{2}

, which is option D.

Answer:

x=\frac{3}{2}

i.e. option D.

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