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Question

If two chords drawn from the point A(4,4) to the parabola x2=4y are bisected by the line y=mx, the interval in which m lies is

A
(22,22)
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B
(,2)(2,)
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C
(,222)(222,)
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D
None of these
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Solution

The correct option is C (,222)(222,)
Point (4,4) lies on the parabola.
Let the point of intersection of the line y=mx with the chords be (α,mα).
Then, α=4+x12
x1=2α4
mα=4+y12
y1=2mα4
As (x1,y1) lies on the parabola,
(2α4)2=4(2mα4)
4α2+1616α=8(mα2)
4α28α(2+m)+32=0
For two distinct chords,
D>0
{8(2+m)}24(4)(32)>0
(2+m)2>4×4×3264(2+m)2>8
2+m>22 or
2+m<22
m>222
m<222
m(,222)(222,)

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