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Question

The equation of the parabola whose vertex and focus lie on the xaxis at distances a and a1 (0<a<a1) from the origin respectively, is

A
y2=4(a1a)x
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B
y2=4(a1a)(xa)
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C
y2=4(a1a)(xa1)
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D
none of these
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Solution

The correct option is B y2=4(a1a)(xa)
The coordinates of the focus and vertex of the required parabola are F(a1,0) and V(a,0), respectively.
Therefore, the distance between the vertex and focus is VF=a1a
and so, the the length of the latus rectum =4(a1a).
Thus, the equation of the parabola is
y2=4(a1a)(xa).


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