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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