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Warm Up NO CALCULATOR

Warm Up NO CALCULATOR . 1) Determine the equation for the graph shown . Convert the equation from polar to rectangular. r = 3cos θ + 2sin θ Convert the equation from rectangular to polar. (x + 2) 2 + y 2 = 4. Polar Graphs Homework ANSWERS. Polar Graphs Homework ANSWERS. Parabolas.

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Warm Up NO CALCULATOR

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  1. Warm Up NO CALCULATOR 1) Determine the equation for the graph shown. Convert the equation from polar to rectangular. r = 3cosθ + 2sinθ Convert the equation from rectangular to polar. (x + 2)2 + y2 = 4

  2. Polar Graphs Homework ANSWERS

  3. Polar Graphs Homework ANSWERS

  4. Parabolas Write the equation, focus and directrix of a parabola

  5. Conic Sections • A conic section (or conic) is a cross section of a cone – the intersection of a plane with a right circular cone. • The 3 basic conic sections are the parabola, ellipse and hyperbola. (circle is a special ellipse)

  6. Parabolas • A parabola is the set of all points in a plane equidistant from a particular line (the directrix) and a particular point (the focus)

  7. Equation of a Parabola • The standard (vertex) form equation of a parabola with a vertex at (h, k) and where p represents the directed distance between the focus and vertex (called the focal length).

  8. Identify the direction of the opening • y – 3 = -5(x+1)2 • y2 = -2x • x = -y2 + 3y • 1- 2y + x2 = 0

  9. Examples • Write an equation of the parabola with vertex (2, 1) and focus (2, 4) • Write an equation of the parabola that passes through the point (2, 0) with a vertical axis of symmetry passing through the vertex (3, 1).

  10. Examples (cont.) • Write an equation of the parabola with focus (2, -3) and directrix x = 8

  11. the focal widthof a parabola is the length of the vertical (or horizontal) line segment that passes through the focus and touches the parabola at each end. |4p| is the focal width.

  12. Identify the Parts a) Vertex: b) Opening: c) Axis of Symmetry d) Focal length: e) Directrix: f) Focus: g) Focal width:

  13. Identify the Parts a) Vertex: b) Opening: c) Axis of Symmetry d) Focal length: e) Directrix: f) Focus: g) Focal width:

  14. Completing the Square • First, decide which way your parabola opens(up, down, right or left)! • Is it x = or y = ? Example: • 24x = 4x2 – y + 1

  15. Parts of a Parabola (cont.) • EX: y = 4x2 – 8x + 3 a) Vertex form: b) Vertex: c) Opening: d) Focal length: e) Directrix: f) Focus: g) Focal width:

  16. Parts of a Parabola (cont.) • EX: y2 + 6y + 8x + 25 = 0 a) Vertex form: b) Vertex: c) Opening: d) Focal length: e) Directrix: f) Focus: g) Focal width:

  17. Applications of parabolas

  18. A signal light on a ship is a spotlight with parallelreflected light rays (see the figure). Suppose the parabolicreflector is 12 inches in diameter and 6 inches deep. How far from the vertex should the light source be placed so that the beams of light will run parallel to the axis of its mirror?

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