Question

The point of intersection of the tangents at the point $P$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and its corresponding point $Q$ on the auxiliary circle meet on the line

• A. $x=a/e$
• B. $x=0$
• C. $y=0$
• D. none of these

Answer 1

Answer: (C)

Tangent to the ellipse at point $P(a\cos \theta ,b\sin \theta )$ is
$\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1$ ... (i)
Tangent to the circle at point $Q(a\cos \theta ,a\sin \theta )$ is
$x\cos \theta +y\sin \theta =a$ ..... (ii)
Equations (i) and (ii) intersect at $(a/\cos \theta ,0)$ which lies on $y=0$.