For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$x^{2} = 16 y$

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Solution

Given Equation is $x^{2} = 16 y$
Since, the above Equation is involves $x^{2}$
Its axis is y-axis
Also coefficient of $y$ is positive
$x^{2} = 4 a y$
Comparing
$x^{2} = 16 y$ ........(1)
$x^{2} = 4 a y$ .........(2)
From (1) and (2)
$4 a y = 16 y$
$a = \frac{16 y}{4 y}$
$a = 4$
coorrdinate of focus os (0,a)
$= (0, 4)$
Equation of Directrix is
$y = - a$
$y = - 4$
Lactus Rectum is $y a$
$= 4 \times 4$
$= 16$

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