Q. Length of the straight line $x - 3y = 1$intercepted by the hyperbola $x^{2} - 4y^{2} = 1$ is
A) $\frac{3}{5}\sqrt{10}$
B) $\frac{6}{5}\sqrt{10}$
C) $\frac{5}{3}\sqrt{10}$
D) $\frac{5}{6}\sqrt{10}$
Explanation
(b)
The intersection points of given curves are (1, 0) and $\left( - \frac{13}{5},\ - \frac{6}{5} \right)$
$\therefore$ The distance between these two points
$= \sqrt{\left( 1 + \frac{13}{5} \right)^{2} + \left( 0 + \frac{6}{5} \right)^{2}}$
$= \frac{1}{5}\sqrt{324 + 36}$
$= \frac{6}{5}\sqrt{10}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.