1 / 18

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.

osma
Download Presentation

Warm Up NO CALCULATOR

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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?

More Related