Let P, Q, R, S be the points of intersection of the circle $x^2 + y^2 = 4$ and the hyperbola $xy = \sqrt{3}$. If P = $(\alpha,\beta)$ and $\alpha>\beta>0$, then the equation of the tangent drawn at P to the hyperbola is
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The equation of the tangent to a rectangular hyperbola $xy=c^2$ at a point $(x_1, y_1)$ can be remembered as $\frac{x}{x_1} + \frac{y}{y_1} = 2$, or more commonly as $xy_1+yx_1=2c^2$.