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:

$y^{2}=12 x$

 

Solution:

Given equation : $y^{2}=12 x$

Comparing given equation with parabola having equation,

$y^{2}=4 a x$

$4 a=12$

- $a=3$

Focus :

$F(a, 0)=F(3,0)$

Vertex :

$\mathrm{A}(0,0)=\mathrm{A}(0,0)$

Equation of the directrix : x+a=0

- $x+3=0$

$x=-3$

Lenth of latusrectum : $4 \mathrm{a}=4 .(3)=12$

 

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