Question

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

Class X1 - Maths -Conic Sections Page 246

Answer 1

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

Here, x² = 6y => x² = 4(3/2)y , on comparing it with equation x² = 4ay . we get , a = 3/2

Hence,
co-ordinate of focus ( 0, a) = ( 0, 3/2)
axis of the parabola = Y -axis
the equation of directrix , y = -a = -3/2
Length of Latusrectum = 4a = 4 × 3/2 = 6