Question

For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$x^2=-9y$

Answer 1

Given equation is $x^2=-9y$

Since the above equation is involves $x^2$

Its axis is x-axis

Also coefficient of y-axis is Positive.

Hence, we use equation

$y^2=-4ay

Comparing

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

$x^2=-4ay$.......(2)

From (1) and (2)$

$-4ay=-9y$

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

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

Coordinate of four is (0,-a)

$=(0,\frac{-9}{4})$

Equation of Direction is

$y=a$

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

Lactus Rectum is $4a$

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

$=9$