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The equation to the chord joining two points(x_{1}, y_{1}) \:\:and\:\: (x_{2}, y_{2}) on the rectangular hyperbola xy=c^{2}   is :

Option: 1

\frac{x}{x_{1}+x_{2}}+\frac{y}{y_{1}+y_{2}}=1


Option: 2

\frac{x}{x_{1}-x_{2}}+\frac{y}{y_{1}-y_{2}}=1


Option: 3

\frac{x}{y_{1}+y_{2}}+\frac{y}{x_{1}+x_{2}}=1


Option: 4

\frac{x}{y_{1}-y_{2}}+\frac{y}{x_{1}-x_{2}}=1


Answers (1)

best_answer

 

Rectangular Hyperbola -

x^{2}-y^{2}= a^{2}

- wherein

 

 

Mid point is M\left ( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2} \right )

\therefore equation of the chord to the hyperbola  xy=c^{2}

 

 whose midpoint is M, is     \frac{x}{\frac{x_{1}+x_{2}}{2}}+\frac{y}{\frac{y_{1}+y_{2}}{2}}=2

\frac{x}{x_{1}+x_{2}}+\frac{y}{y_{1}+y_{2}}=1

Posted by

rishi.raj

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