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

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IIT JEE Trainer

Asymptotes are nothing but tangents at infinity take equation of tangents and solve it.
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IIT JEE Trainer

Let equation of the hyperbola is (x-h)^2/a^2+(y-b)^2/b^2 and its asymptotes are given by:- y=+or-(b/a)(x-h)+k. You can compare your equations with this and find relevant values of a, b, h, k and substitute in equation of hyperbola.
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Define asymptote?
It is a line such that the distance between the curve and the line approaches zero as they tend to infinity.an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity.
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Eccentricity is define as the ratio of the distance of any point on a conic section from a focus to its distance from the corresponding directrix and it is denoted with "e"; e range from 0 to 1; 0 < e <1.
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