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  • A tangent to the parabola  meets the hyperbola <img alt="\mathr

A tangent to the parabola \mathrm{x^2=4 a y} meets the hyperbola \mathrm{x^2-y^2=a^2}  at two points P and Q, then midpoint of P and Q lies on the curve.

 

Option: 1

\mathrm{ y^3=x(y-a) }


Option: 2

\mathrm{y^3=x^2(y-a)}


Option: 3

\mathrm{y^2=x^2(y-a)}


Option: 4

\mathrm{y^2=x^3(a-y)}


Answers (1)

best_answer

Equation of tangent to parabola \mathrm{y=m x-a m^2 \ldots \ldots(1)}equation of chord of hyperbola whose midpoint is (h, k) is   \mathrm{h x-k y=h^2-k^2 \ldots \ldots(2)} form (1) and  (2)
\mathrm{\frac{m}{h}=\frac{1}{k}=\frac{a m^2}{h^2-k^2} \Rightarrow k^3=h^2(k-a)}

Posted by

vishal kumar

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