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A hyperbola has its centre at the origin...

A hyperbola has its centre at the origin, passes through the point (4, 2) and has transverse axis of length 4 along the x-axis. Then the eccentricity of the hyperbola is

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Knowledge Check

  • If the normal at the point P intersects the x-axis at (9, 0) then the eccentricity of the hyperbola is

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

  • The line 2x + y = 1 touches a hyperbola and passes through the point of intersection of a directrix and the x-axis. The equation of the hyperbola is

    A
    `(x^(2))/(1)-(y^(2))/(3)=1`
    B
    `(x^(2))/(1)-(y^(2))/(3)=2`
    C
    `(x^(2))/(3)-(y^(2))/(1)=1`
    D
    `(x^(2))/(3)-(y^(2))/(1)=2`

  • The foci of a hyperbola are (pm 5, 0) and its transverse axis is of length 8. The equation of the hyperbola is-

    A
    `(x^2)/( 16) - (y^2)/( 9) = 1`
    B
    `(x^2)/( 9) - (y^2)/( 16) =1`
    C
    `(x^2)/( 25)- (y^2)/( 16) =1`
    D
    `(x^2)/( 16) - (y^2)/(25) =1`

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