Q.

If the normal at (ct1, c/t1) on the hyperbola xy = c2 cuts the hyperbola again at (ct2, c/t2), then t1t2   3=
 

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a

2

b

–2 
 

c

1

d

–1 
 

answer is C.

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Detailed Solution

Given hyperbola xy=c2

let P=ct1, ct1 be any point on this hyperbola.

Now equation of normal at 'P' is y-ct1=t12(x-ct1)

yt1-xt13-c+ct14=0

since it passes through ct2, ct2 then

ct2 t1-(ct2) t13-c+ct14=0 ct13 (t1-t2)-c1-t1t2=0 ct13(t1-t2)+c(t1-t2)t2=0 (t1-t2) ct13+ct2=0 ct13+ct2=0 (t1t2) ct13=-ct2 t13 t2=-1. 

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If the normal at (ct1, c/t1) on the hyperbola xy = c2 cuts the hyperbola again at (ct2, c/t2), then t1t2   3=