MAT136H1 Lecture Notes - Polar Coordinate System
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MAT136H1 Full Course Notes
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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.
