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There are exactly two points on the elli...

There are exactly two points on the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` whose distances from its center are the same and are equal to `(sqrt(a^2+2b^2))/2dot` Then the eccentricity of the ellipse is `1/2` (b) `1/(sqrt(2))` (c) `1/3` (d) `1/(3sqrt(2))`

A

`1//2`

B

`1//sqrt(2)`

C

`1//3`

D

`1//3sqrt(2)`

Text Solution

AI Generated Solution

To solve the problem, we need to find the eccentricity of the ellipse given the condition about the distances from its center. The equation of the ellipse is given by: \[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \] ...
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