Question

Find co-ordinate of focus, equation of directrix, length of latus rectum and the co-ordinate of end points of latus rectum of the parabola:

x² = –8y

Answer 1

The equation of the parabola is x² = –8y.

Comparing with x² = – 4by, we get,

4b = 8

∴ b = 2

The coordinates of the focus are (0, – b), i.e. (0, – 2).

The equation of the directrix is

y – b = 0, i.e. y – 2 = 0

The length of the latus rectum = 4b = 8

The coordinates of the end points of the latus rectum are (2b, –b) and (–2b, –b) i.e., (4, – 2) and (– 4, – 2).