hyperbola

the normal to the rectangular hyperbola xy=c^2 at the point t1 meets the curve again at t2. value of ti^3.t2 is

1 Answers

equation of a normal is

at t1 is

y-c/t1=t1²(x-ct1)

if it meets the parabola again at t2

c/t2-c/t1=t1²(ct2-ct1)

c(t1-t2)/t2t1=t1²c(t2-t1)

so cancel c from both sides..

t1³t2 = -1

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

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