Let p be the perpendicular distance from the centre C of the hyperbola x²/a² - y²/b² = 1 to the tangent at a point R on it. If S and S' are the foci and (RS - RS')² = lambda*a²*(1 + b²/p²)... in the standard result (RS)(RS') =... the relation is (RS)(RS') = lambda*a²*(1 + b²/p²). Find lamb

Question

Let p be the perpendicular distance from the centre C of the hyperbola x²/a² - y²/b² = 1 to the tangent at a point R on it. If S and S' are the foci and (RS - RS')² = lambda*a²*(1 + b²/p²)... in the standard result (RS)(RS') =... the relation is (RS)(RS') = lambda*a²*(1 + b²/p²). Find lambda.

Accepted Answer

1. The standard hyperbola identity gives (RS)(RS') = a²(1 + b²/p²), so the constant lambda equals 1.

Let p be the perpendicular distance from the centre C of the hyperbola x²/a² - y²/b² = 1 to the tangent at a point R on it. If S and S' are the foci and (RS - RS')² = lambdaa²(1 + b²/p²)... in the standard result (RS)(RS') =... the relation is (RS)(RS') = lambdaa²(1 + b²/p²). Find lambda.

Solution

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