# Ex.11.2 Q4 Conic Sections - NCERT Maths Class 11

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## Question

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for $${x^2} = - 16y$$.

## Text Solution

The given equation is $${x^2} = - 16y$$

Here, the coefficient of $$y$$ is negative.

Hence, the parabola opens downwards.

On comparing this equation $${x^2} = - 4ay$$, we obtain

$- 4a = - 16 \Rightarrow a = 4$

Therefore,

Coordinates of the focus $$F = \left( {0, - a} \right) = \left( {0, - 4} \right)$$

Since the given equation involves $${x^2}$$, the axis of the parabola is the $$y$$-axis.

Equation of directrix, $$y = a$$ i.e., $$y = 4$$

Length of latus rectum $$4a = 4 \times 4 = 16$$

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