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:

5y² = 24x

Answer 1

Given equation of the parabola is 5y² = 24x.

∴ y² = `24/5"x"`

Comparing this equation with y² = 4ax, we get

4a = `24/5`

∴ a = `6/5`

Co-ordinates of focus are S(a, 0), i.e., S`(6/5, 0)`

Equation of the directrix is x + a = 0.

i.e., `"x" + 6/5` = 0, i.e., 5x + 6 = 0

Length of latus rectum = 4a = `4(6/5) = 24/5`

Co-ordinates of end points of latus rectum are (a, 2a) and (a, –2a), i.e., `(6/5, 12/5)` and `(6/5, (-12)/5)`.