Length of latus rectum of parabola $x^{2} = 4 a y$ is equal to double the distance between focus and foot of directrix.

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x^{2}

= - 16 y

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

How many of the following statements are correct?

(a) The focus of $x^{2} = 4 a y$ is (0, a)

(b) The directrix of $y^{2} = - 4 a x$ is x + a = 0

(d) The parabolas $x^{2} = 4 a y$ and $y^{2} = 4 a x$ are equal.

x^{2} - 2 x + 8 y + 17 = 0

y^{2} = - 12 x

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