Go Over and Check Homework

Algebra 2B Day 22

10.4 Ellipses

·  Daily Openers

·  Go over and check homework

·  Hand back amortization problem

10.4 Ellipses

Ellipse – set of all points (x, y) & the sum of the distances between (x, y) and the TWO distinct fixed point (focuses or foci) is a constant.

Vertices – two points that are intersected by the line through the foci.

Major Axis – line segment joining the vertices. Its midpoint is the center of the ellipse.

Minor Axis – line segment to major axis at the center. Endpoints called Co-vertices

-Draw and label an ellipse

Standard Equation of an Ellipse (Center at Origin)

The standard form of an ellipse with center at (0, 0) and major axes length (2a) and minor axes length (2b), where a>b is:

Horizontal major axis

Vertical major axis

The vertices on a major axis, a units from center. The co-vertices on minor

Axis, b units from the center.

The foci, on major axis, are c units from center; where .

·  Orientations:

Ex. Find the foci and vertices: Ex. Find the foci and vertices:

Ex. Write the equation in standard form: Ex. Write the equation in standard form

+y

Ex. Find an equation of an ellipse with center (0,0) and: Ex. Find an equation of an ellipse with center (0,0) and: Vertex: (0,4) Vertex: (-5,0)

Co-vertex: (3,0) Co-vertex: (-4,0)

Homework – pages 571-572 #1-63 Odd

Daily Openers – 1. Draw the Circle:

2. Find the center and radius of the circle:

3. Find the focus and directrix:

4-5. Find the point(s) of intersection: