Question

Find the coordinate of focus, equation of directrix, length of latus Rectum and coordinate of end point of latus rectum for the parabola.
$y^2=20x$.

Answer 1

$y^2=20x$

$\Rightarrow y^2=4\left(s\right)x$

$\therefore$ From general eqn of parabola $y^2=4ax,$

we get, $a=5$

Coordinates of focus$\to (a,0)$

$=(5,0)$

Equation of directrix $\Rightarrow x=-a$

$\Rightarrow x=-5$

$\Rightarrow x+5=0$

Length of latus rectum $\to 4a$

$4\times 5=20$

Coordinates of end points of

latus rectum are $(a,2a)\&(a,-2a)$

$\to (5,10)\&(5,-10)$ Ans.