10.5 Parametric Equations & Polar Coordinates

Conic Sections

Question #1 (Easy): Vertex, Focus, Directrix for Parabola

Strategy

For a parabola equation , or the focus is at or and the directrix is

or , respectively. The focus can shift horizontal and vertically in the opposite direction of

the numeric values added unto and .

Sample Question

Find the vertex, focus, and directrix of the parabola and sketch the graph.

Solution

The equation can be re-written in the form of ,

which means the vertex is at and since the parabola is in the form

of , , . Then the directrix is , which

means 3 units down from the vertex. Thus because of the shift of the

vertex, the directrix becomes . The focus is directly above

the vertex, but moved in the opposite direction, that is in this case

northward by the same unit that directrix is below the vertex. Thus, the

focus is at

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###### Document Summary

Question #1 (easy): vertex, focus, directrix for parabola. For a parabola equation , or the focus is at ( ) or ( ) and the directrix is or , respectively. The focus can shift horizontal and vertically in the opposite direction of the numeric values added unto and . Find the vertex, focus, and directrix of the parabola and sketch the graph. The equation can be re-written in the form of ( ) ( ), which means the vertex is at ( ) and since the parabola is in the form of , , . Then the directrix is , which means 3 units down from the vertex. Thus because of the shift of the vertex, the directrix becomes . The focus is directly above the vertex, but moved in the opposite direction, that is in this case northward by the same unit that directrix is below the vertex.

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