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

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = – 16y

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The given equation is x2 = –16y.

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

On comparing this equation with x2 = – 4ay, we obtain

–4a = –16 ⇒ a = 4

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

Since the given equation involves x2, the axis of the parabola is the y-axis.

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

Length of latus rectum = 4a = 16

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NCERT Class 11 Mathematics Textbook
Chapter 11 Conic Sections
Q 4 | Page 246
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