STD 11 - 10.2 parabola,ellipse,hyperbola — JEE कक्षा 11 साइन्स — Question

$a^{2} x^{2}-y^{2}=b^{2}$ then

$a ^{2} x ^{2}-\left(\frac{\lambda x -\mu}{2}\right)^{2}= b ^{2}$

$\left(4 a ^{2}-\lambda^{2}\right) x ^{2}+2 \lambda \mu x -\mu^{2}-4 b ^{2}=0$

Disc. $=0$

$4 \lambda^{2} \mu^{2}+4\left(4 a ^{2}-\lambda^{2}\right)\left(\mu^{2}+4 b ^{2}\right)=0$

$4 \lambda^{2} b^{2}-4 a^{2} \mu^{2}=16 a^{2} b^{2}$

$\frac{\lambda^{2}}{a^{2}}-\frac{\mu^{2}}{b^{2}}=4$