Circles and Ellipses

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Slide 1  Circle
 A = C
 Both squared terms have the same coefficient

Slide 2  Circle

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

Slide 4
 Add both to both sides
 Center:
 Radius:

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!!

Slide 6  Ellipse
 A ≠ C, but signs must be the same
 Both squared terms have the same sign, different number

Slide 7  Horizontal Ellipses:
 Center (h,k)
 a
 a
 Vertex
 Vertex
 b
 b
 Covertex
 Covertex
 Major
 Axis
 Minor
 Axis
 c
 c
 Focus
 Focus

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

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

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

Slide 11  Center:
 Vertices:
 Covertices:
 Foci:
 Major Length:
 Minor Length:
 Eccentricity:

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

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