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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 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
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
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