Question

The eccentric angles of an ellipse $\alpha ,\beta ,\delta ,\gamma$ are said to be concylic if

• A. $\alpha +\beta +\gamma +\delta =n\pi$
• B. $\alpha +\beta +\gamma +\delta =\pi$
• C. $\alpha +\beta +\gamma +\delta =2n\pi$
• D. None of the above

Answer 1

The correct option is C $\alpha +\beta +\gamma +\delta =2n\pi$

$\theta$ is an eccentric angles, $\left\{\theta ϵ[0,2\pi ]\right\}$

if enncntric angles of an ellipse are $\alpha ,\beta ,\gamma ,\delta$ then for being concyclic,

$\alpha +\beta +\gamma +\delta =2\pi n$ (a complete circle)

As $\alpha ,\beta ,\gamma ,\delta$ are belonging to $[0,2\pi ]$

$\alpha ϵ[0,2\pi ]$

$\beta ϵ[0,2\pi ]$

$\gamma ϵ[0,2\pi ]$

$\delta ϵ[0,2\pi ]$

$\alpha +\beta +\gamma +\delta =2n\pi$