Question

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for $x^2 = - 16y$

Answer 1

The given equation is y^2= 12x.
Here, the coefficient of x is positive.
Hence, the parabola opens towards the right.
On comparing this equation with $y^2 = 4ax,$

we obtain
$4a= 12$
$⇒ a = 3$

∴Coordinates of the focus=$$$ (a, 0) = (3, 0)$Since the given equation involves$y^2$, the axis of the parabola is the x-axis. Equation of direcctrix,$x= -a $i.e.,$x = - 3 $

$x+ 3 = 0$
Length of the latus rectum $= 4a = 12$