Find the hyperbola whose asymptotes are 2x ndash y 3 and 3x y ndash 7 0 and which passes through the...........

Mathematics (NDA) Coordinate Geometry

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

(2x – y – 3)(x + y – 7) = 6.

(2x – y + 3)(3x + y – 7) = 6.

(2x – y – 3)(3x + y – 7) = 6.

(2x +y – 3)(3x + y – 7) = 6.

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

The equation of the hyperbola with asymptotes 3x + y – 7 = 0 and 2x – y = 3 is (3x + y – 7)(2x – y – 3) + k = 0

It passes through (1, 1) k = –6

Hence the equation of the hyperbola is (2x – y – 3)(3x + y – 7) = 6.

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