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Question

The locus of the point which divides the double ordinate of the parabola y2=6ax in the ratio 5:6, is

A
100y2=6ax
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B
144y2=6ax
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C
121y2=6ax
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D
y2121=6ax
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Solution

The correct option is C 121y2=6ax
Let the point P(h,k) divides the double ordinate with end points A(x,y) and B(x,y) in the ratio 5:6.
Then, h=6x+5x11
x=h (i)
and k=6y5y11
y=11k (ii)

Putting (i) and (ii) in parabola y2=6ax, we get
(11k)2=6a(h)
121k2=6ah
Hence, locus of the point is 121y2=6ax

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