The locus a point `P(alpha,beta)` moving under the condition that the line `y=alphax+beta` is a tangent to the hyperbola `x^2/a^2-y^2/b^2=1` is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle

Explanation

To find the locus of the point \( P(\alpha, \beta) \) such that the line \( y = \alpha x + \beta \) is a tangent to the hyperbola given by the equation

\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, \]

we will follow these steps:

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