Find co-ordinates of focus, equation of directrix: 3x^2 = 8y

Question

Find co-ordinates of focus, equation of directrix, length of latus rectum and the coordinates of end points of latus rectum of the parabola: 3x² = 8y

Answer 1

Given equation of the parabola is 3x² = 8y 

⇒ x² = 8/3 y

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, 

⇒ y + 2/3 = 0

⇒ 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),

⇒ (4/3, 2/3) and (- 4/3, 2/3).