Q. If tangent and normal to a rectangular hyperbola $xy = c^{2}$ cut off intercepts $a_{1}\ and\ a_{2}$ on one axis and $b_{1},\ b_{2}$ on the other, then
A) $a_{1} = b_{1}$
B) $a_{2} = b_{2}$
C) $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$
D) $a_{1}a_{2} + b_{1}b_{2} = 0$
Explanation
(d)
Tangent and normal are at$90{^\circ}$.
[image:11_image32.emf]
$\therefore\$Product of slopes is$- 1$.
$\Rightarrow \left( - \frac{b_{1}}{a_{1}} \right)\left( - \frac{b_{2}}{a_{2}} \right) = - 1$
$\Rightarrow a_{1}a_{2} + b_{1}b_{2} = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.