Circles and Ellipses

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Circles and Ellipses

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  1. Circle

    Slide 1 - Circle

    • A = C
    • Both squared terms have the same coefficient
  2. Circle

    Slide 2 - Circle

  3. Ex. 1

    Slide 3 - Ex. 1

    • Complete the Square to change to Vertex Form
    • Divide by the coefficients of x2 and y2
    • Group x2 and x, group y2 and y, move constant to other side
    • Complete the square twice
  4. Slide 4

    • Add both to both sides
    • Center:
    • Radius:
  5. EX. 2 Find Vertex form of a circle with a center at (1,2) containing the point (4,-2).

    Slide 5 - EX. 2 Find Vertex form of a circle with a center at (1,2) containing the point (4,-2).

    • Use Pythagorean Theorem
    • Pause the video here and solve for r!!
  6. Ellipse

    Slide 6 - Ellipse

    • A ≠ C, but signs must be the same
    • Both squared terms have the same sign, different number
  7. Horizontal Ellipses:

    Slide 7 - Horizontal Ellipses:

    • Center (h,k)
    • a
    • a
    • Vertex
    • Vertex
    • b
    • b
    • Covertex
    • Covertex
    • Major
    • Axis
    • Minor
    • Axis
    • c
    • c
    • Focus
    • Focus
  8. Vertical Ellipses:

    Slide 8 - Vertical Ellipses:

    • Center (h,k)
    • a
    • a
    • Vertex
    • Vertex
    • b
    • b
    • Covertex
    • Covertex
    • Major
    • Axis
    • Minor
    • Axis
    • c
    • c
    • Focus
    • Focus
  9. Ex. 1

    Slide 9 - Ex. 1

    • Complete the Square to change to Vertex Form
    • Group x2 and x, group y2 and y, move constant to other side
    • Factor coefficients of x2 and y2
    • Complete the square twice
  10. Slide 10

    • Add the product of the coefficient of x2 and 4, as well as the product of the coefficient of y2 and 1 to the right side ONLY!!
    • Factor Perfect Square Trinomials
    • Divide both sides by the constant term
  11. Center:

    Slide 11 - Center:

    • Vertices:
    • Covertices:
    • Foci:
    • Major Length:
    • Minor Length:
    • Eccentricity:
  12. Ex. 4 Find the equation of an ellipse with a center at (1,2), vertex at (1,-3) and  focus (1,6).

    Slide 12 - Ex. 4 Find the equation of an ellipse with a center at (1,2), vertex at (1,-3) and focus (1,6).

  13. Try this!!!

    Slide 13 - Try this!!!

    • For the ELLIPSE: Graph the ellipse. State the center, foci, length of major and minor axes, vertices, and eccentricity.
    • For the CIRCLE: Graph the circle. State the center and the radius