Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 10x

Solution:

The given equation is

y² = 10x

Here, the coefficient of x is positive.

Hence, the parabola opens towards the right.

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

4a = 10 ⇒ a = 5/2

Therefore,

Coordinates of the focus = (a, 0) = (5/2, 0)

Since the given equation involves y²,

the axis of the parabola is the x-axis.

Equation of directrix, x = - a , i.e., x = - 5/2

Length of latus rectum = 4a = 4 × 5/2 = 10

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 5

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y² = 10x

Summary:

The coordinates of the focus are (5/2, 0), and the axis of the parabola is the x-axis. Hence, The equation of directrix and the length of the latus rectum are - 5/2 and 10, respectively