## Question

Find the hyperbola whose asymptotes are 2*x – y* = 3 and 3*x + y* – 7 = 0 and which passes through the point (1, 1).

### Solution

6

The equation of the hyperbola differs from the equation of the asymptotes by a constant.

The equation of the hyperbola with asymptotes 3*x + y* – 7 = 0

and 2*x – y* = 3 is

(3*x + y* – 7)(2*x – y* – 3) + *k =* 0

It passes through (1, 1) *k* = – 6

Hence the equation of the hyperbola is

(3*x + y* – 7)(2*x – y* – 3) = 6

#### SIMILAR QUESTIONS

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.

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