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:

2y² = 17x

Answer 1

Given equation of the parabola is 2y² = 17x

∴ y² = `17/2"x"`

Comparing this equation with y² = 4ax, we get

4a = `17/2`

∴ a = `17/8`

Co-ordinates of focus are S(a, 0), i.e., S`(17/8, 0)`

Equation of the directrix is x + a = 0

i.e., `"x" + 17/8` = 0, i.e., 8x + 17 = 0

Length of latus rectum = 4a = `4(17/8) = 17/2`

Co-ordinates of end points of latus rectum are (a, 2a) and (a, –2a)

i.e., `(17/8, 17/4)` and `(17/8, -17/4)`