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 :
$x^{2}=16 y$
Solution:
Given equation : $x^{2}=16 y$
Comparing given equation with parabola having equation,
$x^{2}=4 a y$
$4 a=16$
$\cdot a=4$
Focus: $\mathrm{F}(0, \mathrm{a})=\mathrm{F}(0,4)$
Vertex : $A(0,0)=A(0,0)$
Equation of the directrix : $y+a=0$
$-y+4=0$
$\cdot y=-4$
Lenth of latusrectum : 4a = 16
