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Find the equation of the hyperbola which...

Find the equation of the hyperbola which has `3x-4y+7=0` and `4x+3y+1=0` as its asymptotes and which passes through the origin.

Text Solution

Verified by Experts

The combined equation of the asymptotes is
`(3x-4y+7)(4x+3y+1)=0`
`"or "12x^(2)-7xy-12y^(2)+31x+17y+7=0" "(1)`
Since the equation of hyperbola and the combined equation of its asymptotes differ by a constant, the equation of the hyperbola may be taken as
`12x^(2)-7xy-12y^(2)+13x+17y+k=0`
As(2) passes through the origin (0, 0), we have k = 0.
Hence, the equation to the required hyperbola is
`12x^(2)-7xy-12y^(2)+31x+17y=0`
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