Question

Question 6 Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x^2 = –9y

Class X1 - Maths -Conic Sections Page 246

Answer 1

concept : if equation of parabola is in the form of x² = -4ay then,
focus ( 0, - a)
axis of parabola = Y - axis
directrix , y = a
Length of latusrectum = 4a

Here, equation of parabola x² = -9y
x² = -4( 9/4)y , on comparing this equation with equation x² = -4ay
a = 9/4

hence, Focus ( 0, - a) = ( 0, - 9/4)
axis of parabola = Y - axis
directrix , y = a = 9/4
Length of latusrectum = 4a = 4 × 9/4 = 9