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A point P on the ellipse (x^(2))/(2)+(y^...

A point P on the ellipse `(x^(2))/(2)+(y^(2))/(1)=1` is at distance of `sqrt(2)` from its focus s. the ratio of its distance from the directrics of the ellipse is

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Knowledge Check

  • The is a point P on the hyperbola (x^(2))/(16)-(y^(2))/(6)=1 such that its distance from the right directrix is the average of its distance from the two foci. Then the x-coordinate of P is

    A
    `-64//5`
    B
    `-32//9`
    C
    `-64//9`
    D
    none of these

  • 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

    A
    `(1)/(2)`
    B
    `(1)/(2sqrt2)`
    C
    `(1)/(sqrt2)`
    D
    None of these

  • At a point P on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 tangents PQ is drawn. If the point Q be at a distance (1)/(p) from the point P, where 'p' is distance of the tangent from the origin, then the locus of the point Q is

    A
    `(x^(2))/(a^(2))+(y^(2))/(b^(2)) =1+(1)/(a^(2)b^(2))`
    B
    `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1-(1)/(a^(2)b^(2))`
    C
    `(x^(2))/(a^(2))+(y^(2))/(b^(2))=(1)/(a^(2)b^(2))`
    D
    `(x^(2))/(a^(2))-(y^(2))/(b^(2))=(1)/(a^(2)b^(2))`

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    The ecentric angle of the points on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 whose distane from its centre is 2 is/are.

    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

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