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 $\large\frac{x^2}{a^2} -\frac{y^2}{b^2}$$=1$ is

Question

$\begin{array}{1 1}(A)\;a\; hyperbola \\(B)\;a\; parabola \\(C)\;an\; ellipse \\(D)\;a \;circle \end{array}$