Question

For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$y^2=12x$

Answer 1

Given equation is $y^2=12x$

Since the above equation is involves $y^2$

Its axis is x-axis

Also coefficient of x-axis is Positive.

Hence, we use equation

$y^2=4ax$

Comparing

$y^2=12x$.......(1)

$y^2=4ax$.......(2)

From (1) and (2)$

$12x=4ax$

$a=\frac{12x}{4x}$

$a=3$

Coordinate of four is (a,0)

i.e, four (3,0)

Equation of Direction is

$x=-a$

$x=-3$

Lactus Rectum is $4a$

$=4\times 3$

$=12$