Question:
Find the coordinates of the focus and the vertex, the equations of the directrix and the axis, and length of the latus rectum of the parabola :
$x^{2}=-18 y$
Solution:
Given equation : $x^{2}=-18 y$
Comparing given equation with parabola having equation,
$x^{2}=-4 a y$
$4 a=18$
$\cdot a=\frac{9}{2}$
Focus: $F(0,-a)=F\left(0,-\frac{9}{2}\right)$
Vertex: $A(0,0)=A(0,0)$
Equation of the directrix: $y-a=0$
$y-\frac{9}{2}=0$
$y=\frac{9}{2}$
Lenth of latusrectum : $4 \mathrm{a}=18$
