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show that the absolute value of the focal distances of any point P on the hyperbola in the length of its transverse axis.

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Step by step text solution for show that the absolute value of the focal distances of any point P on the hyperbola in the length of its transverse axis. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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Knowledge Check

  • The distance of the point P(a,b,c) from the z axis is

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

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    In an ellipse, the sum of the distances between foci is always less than the sum of focal distances of any point on it. Statement 2 : The eccentricity of any ellipse is less than 1.

    N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the center of the hyperbola the OT.ON is equal to:

    P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tantent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

    Find the eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is (3/4)^("th") of the length of its tranverse axis.

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