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Question

A parabola has x- axis as its axis, y- axis as its directrix and 4a as its latus rectum. If the focus lies to the left side of the directrix then the equation of the parabola is

A
y2=4a(x+a)
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B
y2=4a(xa)
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C
y2=4a(x+a)
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D
y2=4a(x2a)
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Solution

The correct option is D y2=4a(x+a)
Let P(x,y) be a point on the parabola
Given that the directrix is y-axis
So, coordinates of any point M on directrix is of the form (0,y)
Length of latus rectum =4a=2(2a)
Since, axis of parabola is x-axis, and focus is on left side of directrix
So, focus is at (2a,0)
By definition of parabola,
PS=PM
(x+2a)2+y2=x2
y2=4ax4a2
y2=4a(x+a)

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