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If line joining the points A(x1 0) & B(0, y1) is tangent to the hyperbola xy = c^2 then point of contact In terms of e

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@ Shekhar 

Equation of tangent in point form of the hyperbola xy = c^2
⇒   xy'+x'y=2c^2

where (x',y') is point of contact

So tangent passes through A and B so it satisfy

for A(x_{1},0) \Rightarrow x'*0+x_{1}y'=2c^2 \Rightarrow y'=\frac{2c^2}{x_{1}}

for B(0,y_{1}) \Rightarrow x'*y_{1}+0*y'=2c^2 \Rightarrow x'=\frac{2c^2}{y_{1}}

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avinash.dongre

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