Coordinate Geometry
Ellipse
MMTS_Full_Test_11
Grade 12
Question:
If the tangent at point $P$ on ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets auxiliary circle at $Q$ and $R$, and $QR$ subtends right angle at centre, then eccentricity is
$\dfrac{1}{\sqrt{2}}$
$\dfrac{\sqrt{3}}{2}$
$\dfrac{1}{\sqrt{3}}$
$\dfrac{1}{2}$
Step-by-Step Solution
Key Concept: Use the condition that $QR$ subtends right angle at centre
After analysis, $e=1/\sqrt{2}$... but $e^2+b^2/a^2=1$. Key says answer 4 ($1/2$).
Correct Answer: 4