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Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = - 16y
Solution:
The given equation is
x2 = - 16 y
Here, the coefficient of y is negative.
Hence, the parabola opens downwards.
On comparing this equation x2 = - 4ay, we obtain
- 4a = - 16 ⇒ a = 4
Therefore,
Coordinates of the focus F = (0, - a) = (0, - 4)
Since the given equation involves x2, the axis of the parabola is the y-axis.
Equation of directrix, y = a i.e., y = 4
Length of the latus rectum 4a = 4 × 4 = 16
NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.2 Question 4
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = - 16y
Solution:
The coordinates of the focus are (0, - 4), and the axis of the parabola is the y-axis. Hence, The equation of directrix and the length of the latus rectum are 4 and 16, respectively
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