Geometry

Conic Sections

Conics - Parabola - Focus and Directrix

         

The above diagram shows a point PP on a parabola y2=12xy^2=12x with focus FF. If ll is a tangent line to the parabola at point PP, the xx-intercept of ll is QQ, and FPQ=36,\angle FPQ=36^\circ, what is PFQ\angle PFQ in degrees?

Note: The above figure is not drawn to scale.

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

Note: The above diagram is not drawn to scale.

If y=ax+by=ax+b is the equation for a line with slope 66 that is a tangent line of the parabola y2=12xy^2=12x, what is a+b?a+b?

Identify the focus and directrix of the parabola given by x=128y2.x =-\frac{1}{28}y^{2}.

In the diagram above, points P,Q,P, Q, and RR lie on parabola y2=60x.y^2=60x. If the center of gravity of PQR\triangle PQR is the focus FF of the parabola, what is the sum of the lengths PF,QF,\overline{PF}, \overline{QF}, and RF?\overline{RF}?

Note: The figure above is not drawn to scale.

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