Question

Find the coordinates of the focus, the 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 obtain

$4a = 10$

$a = 10/4 = 5/2$

∴Coordinates of the focus = $(a, 0)=(5/2, 0)$
Since the given equation involves $y^2$, the axis of the parabola is the x-axis.
Equation of directrix $x =-a,$

i.e,$x = – 5/2$
Length of latus rectum =$4a= 10.$ (Ans.)