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:
$3 y^{2}=8 x$
Solution:
Given equation :
$3 y^{2}=8 x$
$y^{2}=\frac{8}{3} x$
Comparing the given equation with parabola having equation,
$y^{2}=4 a x$
$4 a=\frac{8}{3}$
- $a=\frac{2}{3}$
Focus: $F(a, 0)=F\left(\frac{2}{3}, 0\right)$
Vertex : $A(0,0)=A(0,0)$
Equation of the directrix : $x+a=0$
$x+\frac{2}{3}=0$
$\mathrm{x}=-\frac{2}{3}$
Lenth of latusrectum : $4 a=\frac{8}{3}$
