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  • The locus of a point  moving under the condition that t

The locus of a point \mathrm{P(\alpha, \beta)} moving under the condition that the line \mathrm{y=\alpha+\beta} is a tangent to the hyperbola \mathrm{\frac{x^2}{a^2}-\frac{y^2}{b^2}=1} is

Option: 1

A parabola
 


Option: 2

An ellipse
 


Option: 3

A hyperbola
 


Option: 4

A circle


Answers (1)

best_answer

If y=m x+c is tangent to the hyperbola then c^2=a^2 m^2-b^2. Here \beta^2=a^2 \alpha^2-b^2. Hence locus of P(\alpha, \beta) is a^2 x^2-y^2=b^2, which is a hyperbola.

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