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If e be the eccentricity of the ellipse ...

If e be the eccentricity of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 ` , then e =

A

`sqrt(1-(b^(2))/(a^(2))`

B

`sqrt(1-(a^(2))/(b^(2))`

C

`sqrt(1+(b^(2))/(b^(2))`

D

`sqrt(1+(a^(2))/(b^(2))`

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The correct Answer is:
A
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A , A' are two vertices S , S' are two foci and e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 . If P be a point on the ellipse such that (Delta A A 'P) /(Delta S S 'P ) = K then _

What is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 if length of its minor axis is equal to the distance between its foci ?

Knowledge Check

  • If e is the eccentricity of the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1 , then e =

    A
    `sqrt(1-(b^(2))/(a^(2)))`
    B
    `sqrt(1+(b^(2))/(a^(2)))`
    C
    `sqrt(1+(a^(2))/(b^(2)))`
    D
    `sqrt(1-(a^(2))/(b^(2)))`

  • If e_1 is the eccentricity of the hyperbola (y^(2))/(b^(2)) - (x^(2))/(a^(2)) = 1 then e_(1) =

    A
    `sqrt(1+(a^(2))/(b^(2)))`
    B
    `sqrt(1-(a^(2))/(b^(2)))`
    C
    `sqrt(1+(b^(2))/(a^(2)))`
    D
    `sqrt(1-(b^(2))/(a^(2)))`

  • The eccentricity of the ellipse 5x^(2) + 9y^(2) = 1 is _

    A
    `(3)/(4)`
    B
    `(sqrt(3))/(2)`
    C
    `(4)/(5)`
    D
    `(2)/(3)`

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    The ellipse (x^(2))/(169) + (y^(2))/(25) = 1 has the same eccentricity as the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 . Find the ratio (a)/(b) .

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    The eccentricity of the ellipse (x -3)^2 + (y-4)^2=y^2/9

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