The locus of a point Pα,β moving under the condition that the line y=αx+β is a tangent to the hyperbola (x^2)/1-(y^2)/(b^2)=1 is a conic, with…

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The locus of a point Pα,β moving under the condition that the line y=αx+β is a tangent to the hyperbola (x^2)/1-(y^2)/(b^2)=1 is a conic, with eccentricity equal to

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Correct answer: (D) √2. The tangent to the hyperbola (x^2)/1-(y^2)/(b^2)=1 is y=mx±√(m^2-b^2) Given that, y=αx+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

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 $\frac{x^{2}}{1} - \frac{y^{2}}{b^{2}} = 1$ is a conic, with eccentricity equal to

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The locus of a point Pα,β moving under the condition that the line y=αx+β is a tangent to the hyperbola x21-y2b2=1 is a conic, with eccentricity equal to

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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 $\frac{x^{2}}{1} - \frac{y^{2}}{b^{2}} = 1$ is a conic, with eccentricity equal to