Q. The equation of the normal at the point $(a\sec\theta,\ b\tan{\theta)}\$of the curve$\ b^{2}x^{2} - a^{2}y^{2} = a^{2}b^{2}\$is
A) $\frac{ax}{\cos\theta} + \frac{by}{\sin\theta} = a^{2} + b^{2}$
B) $\frac{ax}{\tan\theta} + \frac{by}{\sec\theta} = a^{2} + b^{2}$
C) $\frac{ax}{\sec\theta} + \frac{by}{\tan\theta} = a^{2} + b^{2}$
D) $\frac{ax}{\sec\theta} + \frac{by}{\tan\theta} = a^{2} - b^{2}$
Explanation
(c)
Equation of normal to hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1\$at
$(a\sec{\theta,\ b\tan{\theta)}\ is\ \frac{ax}{\sec\theta} + \frac{by}{\tan\theta} = a^{2} + b^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.