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The equation of the directrix of the par...

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

A

`x=-1`

B

`x=1`

C

`x=-3/2`

D

`x=3/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `y^(2) + 4y + 4x + 2 = 0`
`implies (y + 2)^(2) + 4x - 2 = 0`
`implies (y + 2)^(2) + 4x - 2 = 0`
`implies (y + 2)^(2) = - 4 (x - (1)/(2))`
Replace `y + 2 = Y, x - (1)/(2) = X`
We have, `Y^(2) = - 4X`
This is a parabola with directrix at X = 1
`implies x - (1)/(2) = 1`
`implies x = (3)/(2)`
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