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


( A ) a hyperbola
( B ) a parabola
( C ) a circle
( D ) an ellipse

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