Question

Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for y${}^2=10x$

Answer 1

The given equation is $y^2=10x$
Here the coefficient of $x$ is positive.
Hence the parabola opens towards the right
On comparing this equation with $y^2=4ax$ , we get
$4a=10$
$\Rightarrow a=\frac{5}{2}$
$\therefore$ Coordinates of the focus $=(a,0)=(\frac{5}{2},0)$
Axis of the parabola is the $x$-axis i.e $y=0$
Equation of directrix $x=-a$ i.e.$x=-\frac{5}{2}$
Length of latus rectum $=4a=10$