Question

The eccentric angles of the extremities of latus recta of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 are given by

• A. tan^-1$\left( \pm \frac{ae}{b} \right)$
• B. tan^-1$\left( \pm \frac{be}{a} \right)$
• C. tan^-1$\left( \pm \frac{b}{ae} \right)$
• D. tan^-1$\left( \pm \frac{a}{be} \right)$

Answer 1

Answer: (C)

tan^-1$\left( \pm \frac{b}{ae} \right)$

Answer 2

Coordinates of any point on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1 whose eccentric angle is θ are (a cos θ, b sin θ). The coordinates of the end points of latus recta are $\left( ae, \pm \frac{b^{2}}{a} \right)$. ∴ acosθ = ae and b sin θ = ± $\frac{b^{2}}{a}$

⇒ tan θ = ±$\frac{b}{ae}$ ⇒ θ tan^-1 $\left( \pm \frac{b}{ae} \right)$.