Question

The equation of directrix is to the parabola $4x^2-4x-2y+3=0$ will be

• A. $8y=7$
• B. $8x=1$
• C. $8y=5$
• D. $8x=3$

Answer 1

Answer: (A)

$8y=7$

Given parabola, $4x^2-4x-2y+3=0$
$\Rightarrow 4(x^2-x)=2y-3$
$\Rightarrow 4(x^2-x+\frac{1}{4}-\frac{1}{4})=2y-3$
$\Rightarrow {(x-\frac{1}{2})}^2=\frac{2y-2}{4}$
$\Rightarrow {(x-\frac{1}{2})}^2=\frac{(y-1)}{2}$
which is of the form
$X^2=4aY$
where, $X=x-\frac{1}{2}$ and $Y=y-1$
and $a=\frac{1}{8}$
$\therefore Directrix,Y+a=0$
$\Rightarrow y-1+\frac{1}{8}=0$
$\Rightarrow y-\frac{7}{8}=0$
$\Rightarrow 8y=7$