Question

If the equation of parabola is $x^2=-9y$, then the equation of the directrix and the length of latus rectum are

• A. $y=-\frac{9}{4},8$
• B. $x=\frac{-9}{4},9$
• C. $y=\frac{9}{4},9$
• D. $Noneofthese$

Answer 1

The correct option is C $y=\frac{9}{4},9$

The given equation is of the form $x^2=-4ay$, where a is positive.

Therefore, the focus is on the y-axis in the negative direction and parabola opens downwards.

Therefore,

Given equation of parabola-

$x^2=-9y.....\left(1\right)$

Standard equation of parabola-

$x^2=-4ay.....\left(2\right)$

Comparing ${eq}^n\left(1\right)\&\left(2\right)$, we have

$a=\frac{9}{4}$

As we know that, for parabola in the form $x^2=-4ay$, equation of directrix for parabola is-

$y=a$

$\therefore$ For $x^2=-9y$, equation of directrix is-

$y=\frac{9}{4}$

Length of latus rectum, $l=4a$

As $a=\frac{9}{4}$,

$\therefore l=4\times \frac{9}{4}=9$

Hence, the equation of directrix will be $y=\frac{9}{4}$ and the lngth of latus rectum will be 9.