Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = - 9y

Solution:

The given equation is x² = - 9y

Here, the coefficient of y is negative.

Hence, the parabola opens downwards.

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

- 4a = - 9 ⇒ a = 9/4

Therefore,

Coordinates of the focus = (0, - a) = (0, 9/4)

Since the given equation involves x²,

the axis of the parabola is the y - axis.

Equation of directrix, y = a, i.e., y = 9/4

Length of latus rectum = 4a = 4 × 9/4 = 9

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 6

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = - 9y

Summary:

The coordinates of the focus are (0, 9/4), and the axis of the parabola is the y-axis. Hence, The equation of directrix and the length of the latus rectum are 9/4 and 9, respectively