#### 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} = – 16*y*

#### Solution

The given equation is *x*^{2} = –16*y*.

Here, the coefficient of *y *is negative. Hence, the parabola opens downwards.

On comparing this equation with *x*^{2}* = – *4*ay, *we obtain

–4*a* = –16 ⇒ *a* = 4

∴Coordinates of the focus = (0, –*a*) = (0, –4)

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 = 4*a* = 16

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Solution Find the Coordinates of the Focus, Axis of the Parabola, the Equation of Directrix and the Length of the Latus Rectum for X2 = – 16y Concept: Parabola - Latus Rectum.