If the latus rectum of an ellipse makes anequilateral triangle at the

1.	If the latus rectum of an ellipse makes anequilateral triangle at the centre then e =
Answer» The ECCENTRICITY e of the ellipse is √3/2 Step-by-step explanation: Let the ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ Any point on the ellipse will be $(a\cos\tehta, b\sin\theta)$ If the latus rectum of ellipse MAKES an equilateral triangle Then the major axis will BISECT its one of the angle which will be equal to $30^\circ$ Therefore, we can say that one vertex of the triangle that lies on the ellipse will be $(\a\cos 30^\circ, b\sin 30^\circ)$ or, $(\frac{\sqrt{3}a}{2}, \frac{b}{2})$ The focus of the ellipse will be $(\frac{\sqrt{3}a}{2}, 0)$ But We know that focus of ellipse is $(ae, 0)$ Therefore, comparing both we get $e=\sqrt{3}/2$ Hope this answer is helpful. Know More: Q: If the LENGTH of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3 2 units, then its eccentricity is: Click Here: brainly.in/question/7470205

If the latus rectum of an ellipse makes anequilateral triangle at the centre then e =

Answer»

The ECCENTRICITY e of the ellipse is √3/2

Step-by-step explanation:

Let the ellipse be

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Any point on the ellipse will be $(a\cos\tehta, b\sin\theta)$

If the latus rectum of ellipse MAKES an equilateral triangle

Then the major axis will BISECT its one of the angle which will be equal to $30^\circ$

Therefore, we can say that one vertex of the triangle that lies on the ellipse will be

$(\a\cos 30^\circ, b\sin 30^\circ)$

or, $(\frac{\sqrt{3}a}{2}, \frac{b}{2})$

The focus of the ellipse will be $(\frac{\sqrt{3}a}{2}, 0)$

But

We know that focus of ellipse is $(ae, 0)$

Therefore, comparing both we get

$e=\sqrt{3}/2$

Hope this answer is helpful.

Know More:

Q: If the LENGTH of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is 3 2 units, then its eccentricity is:

Click Here: brainly.in/question/7470205