Question

Find the equation of the parabola with focus (6, 0) and directrix x = -6. Also find the length of latus-rectum

Answer 1

We have,

Equation of parabola

$y^2=4ax$

Focus has positive x co ordinate.

So,

Co ordinate of focus $=(a,0)$

$(a,0)=(6,0)$

$a=6$

Hence, equation of parabola is

$y^2=4ax$

$y^2=4\times 6x$

$y^2=24x$

Then,

Latus rectum $=4a=4\times 6=24$

Hence, this is the answer.