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:

y² = –20x

Answer 1

The equation of the parabola is y² = –20x.

Comparing with y² = –4ax, we get

4a = 20

∴ a = 5

The coordinates of the focus are (– a, 0) i.e (– 5, 0)

The equation of the directrix is x – a = 0 i.e. x – 5 = 0

Length of latus rectum = 4a = 20

The coordinates of the end points of latus rectum are (–a, 2a) and (– a, – 2a) i.e. (– 5, 10) and (– 5,  –10).