Question

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

• A. $x = - 1$
• B. $x = 1$
• C. $x = \frac { - 3 } { 2 }$
• D. $x = \frac { 3 } { 2 }$

Answer 1

Answer: (D)

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

Answer 2

Here, $y ^ { 2 } + 4 y + 4 + 4 x - 2 = 0$ or $( y + 2 ) ^ { 2 } = - 4 \left( x - \frac { 1 } { 2 } \right)$

Let $y + 2 = Y$ , $\frac { 1 } { 2 } - x = X$. Then the parabola is $Y ^ { 2 } = 4 X$.

∴ The directrix is $X + 1 = 0$ or $\frac { 1 } { 2 } - x + 1 = 0$ ,

∴$x = \frac { 3 } { 2 }$