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:
$y^{2}=10 x$
Solution:
Given equation: $\mathrm{y}^{2}=10 \mathrm{x}$
Comparing given equation with parabola having equation,
$y^{2}=4 a x$
$4 a=10$
$\cdot a=2.5$
Focus : $F(a, 0)=F(2.5,0)$
Vertex : $A(0,0)=A(0,0)$
Equation of the directrix : $x+a=0$
- $x+2.5=0$
- $x=-2.5$
Lenth of latusrectum : $4 \mathrm{a}=4 \cdot(2 \cdot 5)=10$
