HyperbolaHard
Question
If the normal to the rectangular hyperbola xy = c2 at the point ′t′ meets the curve again at ′t1′ then t3t1 has the value equal to -If the normal to the rectangular hyperbola xy = c2 at the point ′t′ meets the curve again at ′t1′ then t3t1 has the value equal to -
Options
A.1
B.-1
C.0
D.none
Solution
Equation of normal of rectangular hyperbola
xy = c2 at P(ct, c/t) will be
y -
= t2 (x - ct)
as it also passes through t1
⇒ c
= ct2 (t1 - t)
⇒ t3t1 = - 1
xy = c2 at P(ct, c/t) will be
y -
= t2 (x - ct)as it also passes through t1
⇒ c
= ct2 (t1 - t)⇒ t3t1 = - 1
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