Find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation by hand.
Vertex is at and focus is at .
The equation of a parabola is
The points are .
The graph of an equation is
The given vertex is at and focus is at .
The vertex is at and focus both lie on the horizontal line (the axis of symmetry). The distance a from the vertex to the focus is .
The parabola opens to the right. The form of a equation is
where and . Therefore, the equation is
The two points that determines the latus rectum by letting , so that
The points are and .
The graph of a parabola is
Semi elliptical Arch Bridge The arch of a bridge is a semi ellipse with a horizontal major axis. The span is feet, and the top of the arch is feet above the major axis. The roadway is horizontal and is feet above the top of the arch. Find the vertical distance from the roadway to the arch at -foot intervals along the roadway.
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