Transcription of Section 9.3 The Parabola Objectives
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Section 9.3 The Parabola Objectives
900 Chapter 9 Conic Sections and Analytic as a quadraticequation in and then use the quadratic formula to express in terms of Graph the resulting two equations using agraphing utility in a by viewingrectangle. What effect does the have on the graph ofthe resulting hyperbola? What problems would youencounter if you attempted to write the given equation instandard form by completing the square? and in the same viewingrectangle. Explain why the graphs are not the Thinking ExercisesMake Sense?In Exercises 81 84, determine whether eachstatement makes sense or does not make sense, and explain changed the addition in an ellipse s equation to subtractionand this changed its elongation from horizontal to noticed that the definition of a hyperbola closely resemblesthat of an ellipse in that it depends on the distances betweena set of points in a plane to two fixed points, the graphed a hyperbola centered at the origin that hadbut no graphed a hyperbola centered at the origin that wassymmetric with respect to the and also symmetricwith respect to the ,x x 16-y y 9=1x216-y29=1xy-term3-30, 50, 1043-50, 70, +2y2-3x+10y-6=0In Exercises 85 88, determine
The rectangular coordinate system enables us to translate a parabola’s geometric definition into an algebraic equation.Figure 9.30is our starting point for obtaining an equation. We place the focus on the at the point The directrix has an equation given by The vertex,located midway between the focus and the directrix,is at the origin.
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