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Question

If the normal at (ct,ct) on the curve xy=c2 meets the curve again in t′, then

A
t=1t3
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B
t=1t
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C
t=1t2
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D
t2=1t2
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Solution

The correct option is A t=1t3
xy=c2 and point (ct, c/t)
Let us equation of the normal
y=c2x
dydx=c2x2
hence slope of normal is given by x2c2 & (ct , c/t) is
t2 and its equation is
y=t2(xct)+c/t
xt3ytct4+c=0
At this passes through (ct1,c/t1)
ct1.t3ct1.tct4+c=0
ct3.(t1t)+ct1(t1t)=0
(ct3+ct1)(t1t)=0
ct3+ct1=0 ct3=ct1
t3=1t1
t1=1t3

1167871_1248180_ans_0c334639e53040f288bed9e962b3b39b.jpg

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