SATHEE: Parabola 1 Question 9

Parabola 1 Question 9

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

(2001, 1M)

(a) $x = - 1$

(b) $x = 1$

(d) $x = 3 / 2$

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Answer:

Correct Answer: 9. (d)

Solution:

Given,

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

$\Rightarrow$

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

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

Replace $y + 2 = Y, x - \frac{1}{2} = X$

We have,

$Y^{2} = - 4 X$

This is a parabola with directrix at $X = 1$

$\begin{array}{lc} \Rightarrow & x - \frac{1}{2} = 1 \\ \Rightarrow & x = \frac{3}{2} \end{array}$

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Parabola 1 Question 9

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

Answer:

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