Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = - 16y

Solution:

The given equation is

x² = - 16 y

Here, the coefficient of y is negative.

Hence, the parabola opens downwards.

On comparing this equation x² = - 4ay, we obtain

- 4a = - 16 ⇒ a = 4

Therefore,

Coordinates of the focus F = (0, - a) = (0, - 4)

Since the given equation involves x², the axis of the parabola is the y-axis.

Equation of directrix,  y = a i.e., y = 4

Length of the latus rectum  4a = 4 × 4 = 16

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 4

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = - 16y

Solution:

The coordinates of the focus are (0, - 4), and the axis of the parabola is the y-axis. Hence, The equation of directrix and the length of the latus rectum are 4 and 16, respectively