Q. The locus of the point of intersection of the tangents at the end points of the focal chord of an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,\ (b < a)$ is
A) $x = \pm \frac{a^{2}}{\sqrt{a^{2} - b^{2}}}$
B) $y = \pm \frac{b^{2}}{\sqrt{a^{2} - b^{2}}}$
C) $x = \pm \frac{ab}{\sqrt{a^{2} - b^{2}}}$
D) None of these
Explanation
(a)
Since, locus of the point of intersection of the tangents at the end points of a focal chord is directrix
$\therefore$ Required locus is $x = \pm \frac{a}{e} = \pm \frac{a^{2}}{\sqrt{a^{2} - b^{2}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.