Question

Question 4 Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x^2 = – 16y

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 focus ( 0, - a)
axis of the parabola = Y - axis
the equation of the directrix , y = a
Length of Latusrectum = 4a

Here , x² = -16y = -4( 4 )y
on comparing it with the equation y² = -4ay
we get , a = 4

so, co-ordinate of focus ( 0, -a) = ( 0, -4)
axis of parabola = Y -axis
the equation of directrix , y = 4
Length of Latusrectum = 4a = 4 × 4 = 16