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If 7 x^2 + p xy + q y^2 + rx - sy + t = ...

If `7 x^2 + p xy + q y^2 + rx - sy + t = 0` is the equation of the hyperbola whose one focus is (-1,1), eccentricity = 3 and the equation of corresponding directrix is x-y+3 = 0, then value of 't' is :

Text Solution

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`(PF)/(PC)=e`
`(PF)^2=e^2(PC)^2`
`(x+1)^2+(y-1)^2=9|(x-y+3)/sqrt2|^2`
`2x^2+4x+2+2y^2-4y+2=9x^2+9y^2+81-18xy-54y+54x`
`7x^2+7y^2-18xy+50x-50y+77=0`
t=77.
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