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 :

Question

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