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Question

Let the tangent at point P(4,8) to the curve y2=x3 meets the curve again at Q. Then the length of PQ is

A
10
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B
210
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C
310
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D
410
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Solution

The correct option is C 310
Given curve : y2=x3
Let point Q=(t2,t3)
For slope of tangent at P:2ydydx=3x2
So, slope of tangent at P(4,8)= slope of PQ
(dydx)(4,8)=t38t24
3=t38t24
3=(t2)(t2+2t+4)(t2)(t+2)
t2t2=0
t=1,2; (t2)
So, Q(1,1)
PQ=81+9=310

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