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Find the equation of a hyperbola whose a...

Find the equation of a hyperbola whose asymptotes are `2x - y- 3 = 0 and 3x + y - 7 = 0` and which pass through `(1, 1).`

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The equation to a hyperbola differs from the joint equation of its asymptotes by a constant.
`therefore` The equation of the hyperbola is
`(2x - y -3) (3x + y - 7) + k = 0`
This passes through (1, 1)
`therefore (2-1-3)(3+1-7) + k =0`
`therefore k =-6`
Hence the required equation of the hyperlink is
`(2x -y -3)(3x + y - 7) -6 = 0`
or `6x^(2) - xy -y^(2) -23x + 4y + 15 = 0`
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