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:

3y² = –16x

Answer 1

Given equation of the parabola is 3y² = –16x.

∴ y² = `-16/3"x"`

Comparing this equation with y² = – 4ax, we get

4a = `16/3`

∴ a = `4/3`

Co-ordinates of focus are S(–a, 0), i.e., S`(-4/3, 0)`

Equation of the directrix is x – a = 0,

i.e., `"x" - 4/3` = 0 i.e., 3x – 4 = 0

Length of latus rectum = 4a = `4(4/3) = 16/3`

Co-ordinates of end points of latus rectum are (–a, 2a) and (–a, –2a), i.e., `(-4/3, 8/3)` and `(-4/3, -8/3)`.