Question

The directrix of the parabola is

• A. $y-\frac{1}{24}=0$
• B. $y+\frac{1}{2}=0$
• C. $y+\frac{1}{24}=0$
• D. $y+\frac{1}{12}=0$

Answer 1

The correct option is C $y+\frac{1}{24}=0$

Axis of parabola is bisector of parallel chord $AB$ & $CD$ are parallel chords.
So axis will be $x=1$
Equation of parabola is
$(x-1{)}^2=ay+b$
It passes through $(0,1)$ & $(3,3)$
so $1=a+b...\left(1\right)$
& $4=3a+b...\left(2\right)$
from $\left(1\right)$ & $\left(2\right)$
$a=\frac{3}{2}$ & $b=-\frac{1}{2}$
$(x-1{)}^2=\frac{3}{2}(y-\frac{1}{3})$
$a=\frac{3}{8}$

Directrix of $x^2=4ay$ is $y=-a$
$\Rightarrow y-\frac{1}{3}=-\frac{3}{8}$
$\Rightarrow y=\frac{1}{3}-\frac{3}{8}$
$\Rightarrow y+\frac{1}{24}=0$