Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = - 8x

Solution:

The given equation is y² = - 8x

Here, the coefficient of x is negative.

Hence, the parabola opens towards the left.

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

-4a = 8

⇒ a = - 2

Therefore,

Coordinates of the focus

F = (- a, 0) ⇒ (- 2, 0)

Since the given equation involves y²,

the axis of the parabola is the x-axis.

Equation of directrix, x = a , i.e., x = 2

Length of latus rectum = 4a = 4 × 2 = 8

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 3

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = - 8x

Summary:

The coordinates of the focus are (- 2, 0), and the axis of the parabola is the x-axis. Hence, The equation of directrix and the length of the latus rectum are 2 and 8, respectively