Question

The chords of contact of a point p with respect to a hyperbola and its auxiliary circle are at right angle. Then, the point P lies on a. conjugate hyperbola b. one of the directrix c. one of the asymptotes d. None of these

JEE/Engineering Exams

Maths

Solution

116

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chomd of contast i) Slope of chord chard of contact of ( P ) wastot. Jhe anxiliary The chard of convals is hxtry ( =a^{2}-b^{2}-c(1 i) ) circle is hxtkd slope of chord of ( =frac{-h}{k} ) Nou), ( frac{h b^{2}}{k q^{2}} timesleft(frac{-h}{k}right)=-1 ) ( Rightarrow quad h^{2} b^{2}-k^{2} s^{2}=0 ) ( Rightarrow frac{h^{2}}{a^{2}}-frac{1 r^{2}}{b^{2}}=0 ) Twolous , P lied on cone of Jho adymptates