If the angle between the tangents drawn to the parabola $y^2=4x$ from the points on the line $4x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is
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The locus of the intersection of tangents to the parabola $y^2=4ax$ that include a constant angle $\theta$ is a hyperbola given by $y^2-4ax = (x+a)^2 \tan^2\theta$. This is known as the director curve (not to be confused with the director circle).