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)

y = 0

Answer 2

Tangent at P and Q are; $\frac{x\cos\theta}{a} + \frac{y\sin\theta}{b} = 1$ and

$\frac{x}{a}\cos\theta + \frac{y}{a}\sin\theta = 1$.

Subtracting, we get $y\sin\theta\left( \frac{1}{b} - \frac{1}{a} \right) = 0$

⇒ y = 0.