Question

The directrix of the parabola y$^2$ + 4x + 3 = 0 is

• A. $x-\frac{4}{3}=0$
• B. $x+\frac{1}{4}=0$
• C. $x-\frac{3}{4}=0$
• D. $x-\frac{1}{4}=0$

Answer 1

Answer: (D)

$x-\frac{1}{4}=0$

Answer 2

The equation of the parabola is
y$^2$ + 4x + 3 = 0
or$\quad\quad\quad y^{2}=-4\left(x+\frac{3}{4}\right)\quad \quad \quad \quad...\left(1\right)$
The directrix of the parabola
$Y^{2}=-4aX\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad... \left(2\right)$
is X = a.
On comparing the equation $\left(1\right)$ and $\left(2\right)$, we
get$\quad\quad4a = 4\quad$ and $X =x+\frac{3}{4}$
or $\quad \quad a = 1\quad$ and $X =x+\frac{3}{4}$
Hence the directrix of the parabola $\left(1\right)$ is
$x+\frac{3}{4}=1 or x-\frac{1}{4}=0.$