Find the vertex, focus, equation of directrix and length of latus rectum of parabola $y^{2} = - 12 x$ .

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Solution

Given $y^{2} = - 12 x$
Since the above equation is involving $y^{2}$
Its axis is $x - a x i s$
Also coefficient of x is negative (-12)
Hence we use equation
$y^{2} = - 4 a x$
Comparing
$y^{2} = - 12 x . . . . (1)$ [Given]
$y^{2} = - 4 a x$
From (1) and (2)
$- 12 x = - 4 a x$
$4 a x = 12 x$
$a = 3$
Coordinates of focus is (-a,0)
i.e focus $(- 3, 0)$
Equation of directix is
$x = a$
$x = 3$
Latus rectum $= 4 a$
$= 4 \times 3$
$= 12$

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