# Circles and Ellipses

Created 3 years ago

Duration 0:23:46
351
Slide Content
1. ### Slide 1 - Circle

• A = C
• Both squared terms have the same coefficient

3. ### 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:
5. ### 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. ### Slide 6 - Ellipse

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

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

• Center (h,k)
• a
• a
• Vertex
• Vertex
• b
• b
• Covertex
• Covertex
• Major
• Axis
• Minor
• Axis
• c
• c
• Focus
• Focus
9. ### 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. ### Slide 11 - Center:

• Vertices:
• Covertices:
• Foci:
• Major Length:
• Minor Length:
• Eccentricity:

13. ### 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