The locus of a point P α , β moving under the condition that the line y = α x + β is a tangent to the hyperbola x 2 1 - y 2 b 2 = 1 is a conic, with eccentricity equal to

Question

The locus of a point P α , β moving under the condition that the line y = α x + β is a tangent to the hyperbola x 2 1 - y 2 b 2 = 1 is a conic, with eccentricity equal to, 1, 2, 1 2, 2

MARKS App · Accepted Answer

The tangent to the hyperbola x 2 1 - y 2 b 2 = 1 is y = m x ± m 2 - b 2 Given that, y = α x + β is a tangent to the hyperbola. So, m = α and m 2 - b 2 = β 2 ∴ α 2 - b 2 = β 2 The locus is x 2 - y 2 = b 2 , which is a hyperbola having eccentricity = 2

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