Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 6y

Solution:

The given equation is

x² = 6 y

Here, the coefficient of y is positive.

Hence, the parabola opens upwards.

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

4a = 6 ⇒ a = 3/2

Therefore,

Coordinates of the focus

F = (0, a) ⇒ (0, 3/2)

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

Equation of directrix, y = - a, i.e., y = - 3/2

Length of latus rectum = 4a = 4 × 3/2 = 6

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 2

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x² = 6y.

Summary:

The coordinates of the focus are (0, 3/2), and the axis of the parabola is the y-axis. Hence, The equation of directrix and the length of the latus rectum are - 3/2 and 6, respectively