Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y ^2 = – 8x

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asked Feb 9, 2018 in Mathematics by Rohit Singh (61,782 points) 35 133 355

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = – 8x

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answered Feb 9, 2018 by sameer (82,980 points) 5 11 37

The given equation is y2 = –8x.
Here, the coefficient of x is negative. Hence, the parabola opens towards the left.

On comparing this equation with y2 = –4ax, we obtain
–4a = –8 ⇒ a = 2
∴Coordinates of the focus = (–a, 0) = (–2, 0)
Since the given equation involves y2, the axis of the parabola is the x-axis.
Equation of directrix, x = a i.e., x = 2
Length of latus rectum = 4a = 8

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