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.

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Originally Posted by jordo6889

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.

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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

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



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