Home
Class 12
MATHS
The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(...

The ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is such that it has the least area but contains the circle `(x-1)^(2)+y^(2)=1`
The eccentricity of the ellipse is

A

` (2sqrt2//3)`

B

`1sqrt(3)`

C

`1//2`

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the eccentricity of the ellipse defined by the equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) that contains the circle defined by \((x-1)^2 + y^2 = 1\) and has the least area. ### Step-by-Step Solution: 1. **Identify the Circle's Properties**: The circle \((x-1)^2 + y^2 = 1\) has its center at \((1, 0)\) and a radius of \(1\). This means the circle extends from \(x = 0\) to \(x = 2\) and from \(y = -1\) to \(y = 1\). 2. **Ellipse Properties**: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is such that its has the least area but contains the circel (x-1)^(2)+y^(2)=1 The length of latus of ellipse is

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

Let there are exactly two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose distance from (0, 0) are equal to sqrt((a^(2))/(2)+b^(2)) . Then, the eccentricity of the ellipse is equal to

The eccentricity of the ellipse x^(2) + 2y^(2) =6 is

The eccentricity of the ellipse (x^2)/25+(y^2)/9=1 is ,

There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2) =1 whose distance from the centre of the ellipse are equal to sqrt((3a^2-b^2)/(3)) . Eccentricity of this ellipse is

There are exactly two points on the ellipse (x^2)/(a^2)+(y^2)/(b^2) =1 whose distance from the centre of the ellipse are equal to sqrt((3a^2-b^2)/(3)) . Eccentricity of this ellipse is

In the ellipse (x^(2))/(6)+(y^(2))/(8)=1 , the value of eccentricity is

Given a > b >0,a_1> b_1>0, area of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is twice the area of ellipse (x^2)/(a_1^ 2)+(y^2)/(b_1^ 2)=1 . If eccentricity of the ellipse is same then: (A) a=sqrt(2)a_1 (B) a a_1=bb-1 (C) a b=a_1b_1 (D) none of these

Given a > b >0,a_1> b_1>0, area of ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is twice the area of ellipse (x^2)/(a_1^2)+(y^2)/(b_1^2)=1 . If eccentricity of the ellipse is same then: (A) a=sqrt(2)a_1 (B) a a_1=bb-1 (C) a b=a_1b_1 (D) none of these