Question

For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$y^2=10x$

Answer 1

Given equation is $y^2=10x$

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

$y^2=10x$.......(1)

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

From (1) and (2)$

$4x=10ax$

$a=\frac{10x}{4x}$

$a=\frac{5}{2}$

Coordinate of four is (a,0)

i.e, four $(\frac{5}{2},0)$

Equation of Direction is

$x=-a$

$x=-\frac{5}{2}$

Lactus Rectum is $4a$

$=4\times \frac{5}{2}$

$=10$