JEE Advance - Mathematics (2005 - No. 14)
Tangents are drawn from any point on the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1$$ to the circle $${x^2} + {y^2} = 9$$.Find the locus of mid-point of the chord of contact.
${{{x^2}} \over 9} - {{{y^2}} \over 4} = {\left( {{{{x^2} + {y^2}} \over 3}} \right)^2}$
${{{x^2}} \over 4} - {{{y^2}} \over 9} = {\left( {{{{x^2} + {y^2}} \over 9}} \right)^2}$
${{{x^2}} \over 9} - {{{y^2}} \over 4} = {\left( {{{{x^2} + {y^2}} \over 9}} \right)^2}$
${{{x^2}} \over 4} - {{{y^2}} \over 9} = {\left( {{{{x^2} + {y^2}} \over 3}} \right)^2}$
${{{x^2}} \over 16} - {{{y^2}} \over 4} = {\left( {{{{x^2} + {y^2}} \over 9}} \right)^2}$