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 :

$y^{2}=-6 x$ 

Solution:

Given equation :

$y^{2}=-6 x$

Comparing given equation with parabola having equation,

$y^{2}=-4 a x$

$4 a=6$

$\cdot a=\frac{3}{2}$

Focus: $F(-a, 0)=F\left(-\frac{3}{2}, 0\right)$

Vertex: $A(0,0)=A(0,0)$

Equation of the directrix : $x-a=0$

$x-\frac{3}{2}=0$

$\mathrm{X}=\frac{3}{2}$

Lenth of latusrectum : $4 a=6$

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