Question

For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$x^2=6y$

Answer 1

Given equation is $x^2=6y$

Since, the above equation is involves $x^2$

Its axis is y-axis

Also coefficient of $y$ is positive

$x^2=6y$, $x^2=4ay$

Comparing

$x^2=6y$.......(1)

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

From (1) and (2)

$4ay=6y$

$=a=\frac{6y}{4y}$

$=a\frac{3}{2}$

Coordinate of focus is (0,a)

$=(0,\frac{3}{2})$

Equation of Directrix is

$y=-a$

$y=\frac{-3}{2}$

Latus Rectum os $4a$

$=4\times \frac{3}{2}$

$=6$