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The equation of the conic with focus at ...

The equation of the conic with focus at ` ( 1,-1) ` directrix along ` x- y +1 ` =0 and with ecuuentricity ` sqrt 2 ` is

A

` x^(2) -y^(2) = 1`

B

` xy =1`

C

` 2xy - 4x + 4y +1=0 `

D

` 2xy +4x -4y -1=0`

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • 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

  • 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
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  • The equation to the parabola having focus (-1,-1) and directrix 2x-3y+6=0 is

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    `x^(2)+6xy+9xy+9y^(2)+28x-16y+46=0`
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    `x^(2)+4xy+4y^(2)-50x+30y+40=0`

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