Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 12x

Solution:

The given equation is y² = 12x

Here, the coefficient of x is positive.

Hence, the parabola opens towards the right.

On comparing this equation with y² = 4ax, we obtain

4a = 12 ⇒ a = 3

Therefore,

Coordinates of the focus F = (a, 0) ⇒ (3, 0)

Since the given equation involves y²,

the axis of the parabola is the x-axis.

Equation of directrix, x = - a , i.e., x = - 3

Length of latus rectum = 4a = 4 × 3 = 12

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 1

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 12x

Summary:

The coordinates of the focus are (3, 0), and the axis of the parabola is the x-axis. Hence, The equation of directrix and the length of the latus rectum are - 3 and 12, respectively