Q. If tangent at any point $P$ on the ellipse ${7x}^{2} + {26y}^{2} = 12$ cuts the tangent at the end points of the major axis at the points $A$ and $B$, then the circle with $AB$ as diameter passes through a fixed point whose coordinates are
A) $\left( \pm \sqrt{a^{2} - b^{2}},\ 0 \right)$
B) $\left( \pm \sqrt{a^{2} + b^{2}},\ 0 \right)$
C) $\left( 0,\ \pm \sqrt{a^{2} - b^{2}} \right)$
D) $\left( 0,\ \pm \sqrt{a^{2} + b^{2}} \right)$
Explanation
The correct answer is Option A: $\left( \pm \sqrt{a^{2} - b^{2}},\ 0 \right)$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.