If the distance between the foci of an ellips | vedclass

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

Question

Given $2 \mathrm{ae}=6 \Rightarrow \quad \mathrm{ae}=3\dots(1)$

and $\frac{2 a}{e}=12 \Rightarrow \mathbb{a}=6 e\dots(2)$

from $( 1)$ and $( 2)$

Vedclass · Accepted Answer

$3\sqrt 2$

Vedclass · Answer

Given $2 \mathrm{ae}=6 \Rightarrow \quad \mathrm{ae}=3\dots(1)$

and $\frac{2 a}{e}=12 \Rightarrow \mathbb{a}=6 e\dots(2)$

from $( 1)$ and $( 2)$

$6 e^{2}=3 \Rightarrow \quad e=\frac{1}{\sqrt{2}}$

$\Rightarrow \quad a=3 \sqrt{2}$

Now, $b^{2}=a^{2}\left(1-e^{2}\right)$

$\Rightarrow \mathrm{b}^{2}=18\left(1-\frac{1}{2}\right)=9$

Length of L.R $=\frac{2(9)}{3 \sqrt{2}}=3 \sqrt{2}$

If the distance between the foci of an ellipse is $6$ and the distance between its directrices is $12$, then the length of its latus rectum is

Similar Questions

An arch is in the form of a semi-cllipse. It is $8 \,m$ wide and $2 \,m$ high at the centre. Find the height of the arch at a point $1.5\, m$ from one end.

An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of the one is the same as the conjugate axis of the other. If $ e_1, e_2 $ be their eccentricities respectively, then $e_1^{ - 2} + e_2^{ - 2}$ equals

The line $y=x+1$ meets the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{2}=1$ at two points $P$ and $Q$. If $r$ is the radius of the circle with $PQ$ as diameter then $(3 r )^{2}$ is equal to

The angle between the pair of tangents drawn from the point $(1, 2)$ to the ellipse $3{x^2} + 2{y^2} = 5$ is

What will be the equation of that chord of ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{9} = 1$ which passes from the point $(2,1)$ and bisected on the point