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# Conics - Parabola - Focus and Directrix

The above diagram shows a point $$P$$ on a parabola $$y^2=12x$$ with focus $$F$$. If $$l$$ is a tangent line to the parabola at point $$P$$, the $$x$$-intercept of $$l$$ is $$Q$$, and $$\angle FPQ=36^\circ,$$ what is $$\angle PFQ$$ in degrees?

Note: The above figure is not drawn to scale.

The above diagram shows a parabola with vertex on the $$y$$-axis, and directrix parallel to the $$y$$-axis. If the focus of the parabola is $$F=(4,6)$$, what is the equation for the parabola?

Note: The above diagram is not drawn to scale.

If $$y=ax+b$$ is the equation for a line with slope $$6$$ that is a tangent line of the parabola $$y^2=12x$$, what is $$a+b?$$

Identify the focus and directrix of the parabola given by $$x =-\frac{1}{28}y^{2}.$$

In the diagram above, points $$P, Q,$$ and $$R$$ lie on parabola $$y^2=60x.$$ If the center of gravity of $$\triangle PQR$$ is the focus $$F$$ of the parabola, what is the sum of the lengths $$\overline{PF}, \overline{QF},$$ and $$\overline{RF}?$$

Note: The figure above is not drawn to scale.

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