Question

Question 3 Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y^2 = – 8x

Class X1 - Maths -Conic Sections Page 246

Answer 1

concept : if equation of the parabola is in the form of y² = -4ax then,
co-ordinate of focus ( -a, 0)
axis of the parabola = X - axis
the equation of directrix , x = a
Length of the Latusrectum = 4a

Here, y² = - 8x = -4( 2 )x
on comparing it with equation y² = -4ax
hence, a = 2

so, co-ordinate of focus ( -a, 0) = ( -2 , 0)
axis of the parabola = X - axis
equation of directrix, x = a = 2
Length of Latusrectum = 4a = 4 × 2 = 8