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Parabola

Parabola. Equation. a is the focal point. a is the focal point. Definition: The set of all points in the plane that are equidistant from a given line and a given point not on that line. Write down the equations of these parabolas and find the focal point. Sketch these parabolas.

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Parabola

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  1. Parabola

  2. Equation

  3. a is the focal point

  4. a is the focal point

  5. Definition:The set of all points in the plane that are equidistant from a given line and a given point not on that line.

  6. Write down the equations of these parabolas and find the focal point.

  7. Sketch these parabolas.

  8. The parametric equations of a parabola are Eliminate t to find the equation of the parabola.

  9. Gallileo

  10. Homework • Exercises 13.3, 13.4 • Delta for experts Exercise 14.7 • Exercise 17.1 • Delta for scholarship • Exercise 17.3 • As the focus moves off to the left, the circle is transformed into an ellipse. At the boundary with the infinite, the ellipse becomes a parabola. The hyperbola is formed on ``other side'' of the infinite.

  11. Kepler's Projective Concept of Conic Sections

  12. Get file from calculus- geometry-geometer’s sketch pad

  13. The intersection of an hyperbola and a parabola determine the magnitudes that double the cube. The parabola is formed from OA=1 and right angle ABD. The hyperbola is formed from the green rectangle OBCD which has an area of 2. From the parabola, OA:OB::OB:OD, or 1:OB::OB:BC. From the hyperbola, OB x BC = 2. Combining these two yields the proportion, 1:OB::OB:BC::BC:2. In other words, line OB will form a cube whose volume is 2 and BC will form a cube whose volume is 4.

  14. Menaechmus' Determination of Two Means by Conic Sections

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