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Find the equation of the parabola whose ...

Find the equation of the parabola whose focus is (-2,3) and directrix is the line 2x+3y-4=0. Also find the length of the latus rectum and the equation of the axis of the parabola.

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The correct Answer is:
`9x^(2) - 12xy + 4y^(2) + 68x - 54y + 153 =0`, length of the latus rectum `= (2)/(sqrt13)` Equation of the axis of the parabola is `3x - 2y + 12=0`
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Knowledge Check

  • Equation of parabola whose focus is (0, 4) and directrix is y + 4 = 0 is

    A
    `y^(2)=16x`
    B
    `y^(2)=8x`
    C
    `x^(2)=16y`
    D
    `x^(2)=8y`

  • The equations of the parabola with focus (0,0) and directrix x+y=4, is

    A
    `x^(2)+y^(2)-2xy+8x+8y-16=0`
    B
    `x^(2)+y^(2)-2xy+8x+8y=0`
    C
    `x^(2)+y^(2)+8x+8y-16=0`
    D
    `x^(2)-y^(2)+8x+8y-16=0`

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