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Question

Question: The equation of the parabola, whose vertex and focus lie on the positive side of the x-axis at dista...

The equation of the parabola, whose vertex and focus lie on the positive side of the x-axis at distances a and a1 from the origin respectively, is

A

y2 = 4(a1 – a)x

B

y2 = 4(a1 – a)(x – a)

C

y2 = 4(a1 – a)(x – a1)

D

None of these

Answer

y2 = 4(a1 – a)(x – a)

Explanation

Solution

The coordinate of the focus and vertex of the required parabola are S(a1, 0) and A(a, 0) respectively. Therefore the distance between the vertex and focus is AS = a1 – a and so the length of the L.R. = 4(a1 – a). Thus, the equation of the parabola referred to the vertex as the origin is y2= 4(a1 – a)x. Now, shifting the origin at (–a, 0), the required equation is Y2 = 4(a1 – a)(X – a). [using y = Y + 0, x = X + (– a)]