Question

ind teh coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=6y$

Answer 1

Teh given equation of parabola is $x^2=6y$
Which is of the form $x^2=4ay.$
$\therefore 4a=6\Rightarrow a=\frac{6}{4}\Rightarrow a=\frac{3}{2}$
$\therefore$
Coordinates of focus are $(0,\frac{3}{2})$
Axis of parabola is x = 0
Equation of thedirectrix is
$y=\frac{-3}{2}\Rightarrow 2y+3=0$
Length of latus rectum $=\frac{4\times 3}{2}=6$