The equation of the parabola whose vertex and focus lie on the x−axis at distances a and a1(0<a<a1) from the origin respectively, is
A
y2=4(a1−a)x
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B
y2=4(a1−a)(x−a)
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C
y2=4(a1−a)(x−a1)
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D
none of these
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Solution
The correct option is By2=4(a1−a)(x−a) 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=a1−a and so, the the length of the latus rectum =4(a1−a). Thus, the equation of the parabola is y2=4(a1−a)(x−a).