Question

Question 8 Find the equation of the parabola that satisfies the following conditions: Focus (0, –3); directrix y = 3

Class X1 - Maths -Conic Sections Page 247

Answer 1

concept :- if focus lies on negative y - axis. I mean Focus ( 0, -a) where a > 0, and equation of directrix is y = a then equation of parabola will be of the form
x² = - 4ay

Here, Focus ( 0, -3) = ( 0, a)
and equation of directrix , y = 3 on comparing with standard equation of directrix , y = a
we get a = 3

hence, equation of parabola
x² = - 4ay
x² = - 4 × 3 × y
x² = - 12y