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One focus of a hyperbola is located at t...

One focus of a hyperbola is located at the point (1, -3) and the corresponding directrix is the line y = 2. Find the equation of the hyperbola if its eccentricity is `(3)/(2)`

Text Solution

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The correct Answer is:
`4x^(2) - 5y^(2) - 8x + 60y + 4 = 0`
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One focus of a hyperbola is located at the point (1,-3) and the corresponding directrix is the line y=2. Find the equation of the hyperbola if its eccentricty is (3)/(2) .

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Knowledge Check

  • One of the foci of the hyperbola is origin and the corresponding directrix is 3x + 4y + 1=0 .The eccentricity of the hyperbola is sqrt 5 .The equation of the hyperbola is

    A
    ` 4x ^(2) + 11y ^(2) + 24xy + 6x + 8y + 1=0`
    B
    ` 8x^(2) + 9y^(2) + 24 xy + 6x + 6y+1 =0`
    C
    ` 8x^(2) + 9y^(2) + 24xy + 6x+ 8y +1=0 `
    D
    ` 8x^(2) + 9y^(2) -24xt + 6x + 8y + 1=0`

  • A conic has latus rectum length 1, focus at (2,3) and the corresponding directrix is x+y -3=0 . Then the conic is

    A
    a parabola
    B
    an ellipse
    C
    a hyperbola
    D
    a rectangular hyperbola

  • i: The equation of the conic with focus at (1,-1) directrix along x-y+1 =0 and with eccentricity sqrt2 is 2xy -4x+ 4y + 1=0 II : One of the foci of the hyperbola is origin and the corresponding directrix is 3x+ 4y + 1=0 .The eccentricity of the hyperbola sqrt 5 .The equation of the hyperbola is 4x^(2) +11y ^(2) + 24xy + 6x+ 8y + 1=0

    A
    only I is true
    B
    only II is true
    C
    both I and II are ture
    D
    neither I nor II true

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    What is the equation to the hyperbola if its latusrectum is (9)/(2) and eccentricity is (5)/(4) ?

    The focus and the correspondin directrix of a hyperbola are (1-3) and y=2 and eccentricity is 3/2. Find the equation of the hyperbola.

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