Question

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

Answer 1

The given equation of apabola is $y^2=10x$
Which is of the form $y^2=4ax.$
$\therefore 4a=10\Rightarrow a=\frac{10}{4}\Rightarrow a=\frac{5}{2}$
Therefore, the coordinates of the focus are $(\frac{5}{2},0)$
Axis of the parabola is y = 0
Equation of the directrix is
$x=\frac{-5}{2}\Rightarrow 2x+5=0$
Length of latus rectum $=\frac{4\times 5}{2}=10$