Find the coordinates of the focus and the vertex, the equations of the

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 : $4 \mathrm{a}=4 \cdot(2 \cdot 5)=10$

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