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Understanding Hyperbola and Parabola: A Comprehensive Review

Learn the concepts of hyperbolas and parabolas, including equations, properties, and graphs in this detailed review. Gain insight into vertices, directrix, focal points, and more.

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Understanding Hyperbola and Parabola: A Comprehensive Review

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  1. Hyperbola and Parabola Review

  2. 1.)

  3. 4.)

  4. 7.) Since we know the graph opens left and right the term with x2 is first.

  5. 8.) Since the x is squared and the p is positive, the graph opens up. That means the focus is 3 units to the up and the directrix is 3 units down. To find another point on the graph, double your p and move that many units from the focus.

  6. 11.)

  7. Write the equation of a parabola with a vertex at (6, 2) and a directrixx=2. 13.) Parabolas open up away from the directrix. Since this parabola opens to the right, the equation has y2 and p is positive. The distance from the directrix to the vertex is 4 so p=4

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