Question

Answer the following:

For the following parabola, find focus, equation of the directrix, length of the latus rectum, and ends of the latus rectum:

5x² = 24y

Answer 1

The equation of the parabola is 5x² = 24y

i.e., x² = `24/5"y"`

Comparing with x² = 4by, we get

4b = `24/5`

∴ b = `6/5`

(1) Focus = (0, b) = `(0, 6/5)`

(2) The equation of directrix is y + b = 0

∴ `"y" + 6/5` = 0

∴ 5y + 6 = 0

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

(4) Ends of latus rectum are (±2b, b) = `(± 12/5, 6/5)`.