If the chord through the point whose eccentri | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Equation of chord to the ellipse with eccentric angle $	heta$ and $\phi$ is given by, $\frac{x}{a} \cos \frac{	heta+\phi}{2}+\frac{y}{b} \sin \frac{

Vedclass · Accepted Answer

$e - 1$

Vedclass · Answer

Equation of chord to the ellipse with eccentric angle $	heta$ and $\phi$ is given by, $\frac{x}{a} \cos \frac{	heta+\phi}{2}+\frac{y}{b} \sin \frac{	heta+\phi}{2}=\cos \frac{	heta-\phi}{2}$

Given it passes through $(a e, 0)$ $\Rightarrow e \cos \frac{	heta+\phi}{2}=\cos \frac{	heta-\phi}{2}$

$\Rightarrow e\left(\cos \frac{	heta}{2} \cos \frac{\phi}{2}-\sin \frac{	heta}{2} \sin \frac{\phi}{2}ight)=\cos \frac{	heta}{2} \cos \frac{\phi}{2}+\sin \frac{	heta}{2} \sin \frac{\phi}{2}$

$\Rightarrow e\left(1-	an \frac{	heta}{2} 	an \frac{\phi}{2}ight)=1+	an \frac{	heta}{2} 	an \frac{\phi}{2}$

$	herefore 	an \frac{	heta}{2} 	an \frac{\phi}{2}=\frac{e-1}{e+1}$

If the chord through the point whose eccentric angles are $\theta \,\& \,\phi $ on the ellipse,$(x^2/a^2) + (y^2/b^2) = 1$ passes through the focus, then the value of $ (1 + e)$ $\tan(\theta /2) \tan(\phi /2)$ is

Similar Questions

Two sets $A$ and $B$ are as under:

$A = \{ \left( {a,b} \right) \in R \times R:\left| {a - 5} \right| < 1 \,\,and\,\,\left| {b - 5} \right| < 1\} $; $B = \left\{ {\left( {a,b} \right) \in R \times R:4{{\left( {a - 6} \right)}^2} + 9{{\left( {b - 5} \right)}^2} \le 36} \right\}$ then : . . . . .

In an ellipse, its foci and ends of its major axis are equally spaced. If the length of its semi-minor axis is $2 \sqrt{2}$, then the length of its semi-major axis is

If a number of ellipse be described having the same major axis $2a$ but a variable minor axis then the tangents at the ends of their latera recta pass through fixed points which can be

If tangents are drawn from the point ($2 + 13cos\theta , 3 + 13sin\theta $) to the ellipse $\frac{(x-2)^2}{25} + \frac{(y-3)^2}{144} = 1,$ then angle between them, is