Questions over Assignment

3R- One more thing we need to do on 8, 9, & 10

Quiz- Open Notes

Conic Sections- Ellipses (Day 1)A conic section is the intersection of a plane and a cone

Ellipse: Given two points F and F' (called the foci), the ellipse is the set of points whose sum of distances to the foci is constant.

Vocabulary

Vocabulary

Center: A point inside the ellipse which is the midpoint of the line segment linking the two foci. The intersection of the major and minor axes.

Vocabulary

Major/Minor Axis: The longest and shortest diameters of an ellipse.

Vocabulary

Focus Points/Foci: The points from which the ellipse is defined. “The ellipse is the set of points whose sum of distances to the foci is constant.”

P is a point on the Ellipse

Vocabulary

Vertex: Where the Major Axis intersects with the ellipse

Co-Vertex: Where the Minor axis intersects with the ellipse

Equations of Ellipses (Horizontal, Centered at the Origin)

Foci: (-c,0) and (c,0)Vertices: (-a,0) and (a,0)Co-vertices: (0,-b) and (0,b)

Equations of Ellipses (Vertical, Centered at the Origin)

Foci: (0, -c) and (0, c)Vertices: (0, -a) and (0, a)Co-vertices: (-b,0) and (-b,0)

Equ

atio

n fo

r th

e F

oci

Yes, this comes from Pythagorean Theorem. No, the variables used are not the same.No, C is not the hypotenuse.Yes, that can be confusing.No, you do not need to remember where this formula comes from.Yes, you should be able to use it, though.

Example Problem:>Sketch the graph and find the vertices, co-vertices, and foci points for: x² + 4y² = 16

Solution: First put the equation in the correct form by dividing everything by 16: x²/16 + y²/4 = 1 Since the larger value is under x, the ellipse has a horizontal major axis, so a² = 16 and b² = 4. >The values are a = 4, b = 2.>To find c, use c2=a2-b2, c2=16 – 4 c= 3.5

Center at (0, 0) Vertices: (4, 0) and (-4, 0) Co-Vertices: (0, 2) and (0, -2) Foci: (3.5, 0) and (-3.5, 0)

Center at (0, 0) Vertices:  (4, 0) and (-4, 0) End Co-Vertices:  (0, 2) and (0, -2) Foci:  (3.5, 0) and (-3.5, 0) 

Homework…