Question

The equation of a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ at a particular point is $\frac{x}{a} - \frac{y}{b} = \sqrt{2}$. Then the eccentric angle of the point is

• A. π/4
• B. 3π/4
• C. 5π/4
• D. 7π/4

Answer 1

Answer: (D)

7π/4

Answer 2

The equation of tangent at ‘θ’ to the ellipse is

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

The given tangent is $\frac{x}{a}\left( \frac{1}{\sqrt{2}} \right) + \frac{y}{b}\left( \frac{- 1}{\sqrt{2}} \right)$ = 1

∴ Cosθ = $\frac{1}{\sqrt{2}}$, sinθ = -$\frac{1}{\sqrt{2}}$

⇒ θ = 7π/4