Find the focus of the parabola given by the equation -x^2-8x-4y-16=0

The antenna of a radio telescope is a parabloid measuring 54 feet across with a depth of 30 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.

The antenna of a radio telescope is a parabloid measuring 54 feet across with a depth of 30 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.


Sketch the parabola on the xy-plane with the vertex at the origin and its axis along the x-axis. An equation of the parabola is y^{2}=4px

Since the diameter is 54, its radius is 27. Therefore, a point on the parabola is (30,27).

27^{2}=4p(30)

solve for p, the distance from the vertex to the focus.