Find the asymptotes and axes of hyperbola having equation `xy-3y-4x+7=0`.

Answer

Asymptotes; `x-3=-, y-4=0`
Transverse axis: `x-y+1=0`
Conjugate axis: `x+y-7=0`

Explanation

We have hyperbola `(x-3)(y-4)=5`
Clearly, equation of pair of asymptotes is `(x-3)(y-4)=0`.
Thus, asymptotes are `x-3=0` and `y-4=0.`
Centre of the hyperbola is (3, 4).
Since hyperbola is rectangular, axes are bisectros of asymptotes having slopes `pm1`.
Therefore, equation of transverse axis is `y-4=1(x-3)` or `x-y+1=0` and equation of conjugate axis is `x+y-7=0`.