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:

3x² = 8y

Answer 1

Given equation of the parabola is 3x² = 8y.

∴ x² = `8/3y`

Comparing this equation with x² = 4by, we get

4b = `8/3`

∴ b = `2/3`

Co-ordinates of focus are S(0, b), i.e., `"S"(0, 2/3)`

Equation of the directrix is y + b = 0,

i.e., `y + 2/3` = 0, i.e., 3y + 2 = 0

Length of latus rectum = 4b = `4(2/3) = 8/3`

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