Algebra II Honors Problem of the DayHomework: p. 799 7, 9, 13, 15, 25-39 odds and worksheet

Paper folding activity is the problem of the day.

Circle - set of all points in a plane equidistant from a given point called the center, ( h, k). The constant distance is called the radius, r.

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x −h( )2 + y− k( )

2 = r2

Parabola- set of all points in a plane that are equidistant from a point called the focus and a line called the directrix.

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y = a x −h( )2 + k x = a y− k( )

2 +h

The distance from vertex to focus and directrix is equal to

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14a

The width of the focal diameter is equal to

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1a

Vertex ( h, k )

Ellipse- set of all points in a plane, the sum of whose distances from two given points, the foci,is a positive constant represented by 2a in the following formulas.

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x −h( )2

a2 +y− k( )

2

b2 =1x −h( )

2

b2 +y− k( )

2

a2 =1

The center is ( h, k ). The foci are c units from the center along the major axis and

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a2 −b2 = c2

The major axis is 2a in length. The endpoints are the vertices.The minor axis is 2b in length.

The eccentricity of an ellipse is an indication of its shape.Eccentricity

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e =ca

Is between 0 and 1. Close to 0 round.

Hyperbola - set of all points in a plane, the difference of whose distances from two given points, the foci, is a positive constant represented by 2a in the following formulas.

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x −h( )2

a2 −y− k( )

2

b2 =1y− k( )

2

a2 −x −h( )

2

b2 =1

The center is at ( h, k ).The foci are c units from the center where

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a2 +b2 = c2

The vertices are the endpoints of the transverse axis which is through the center and 2a units long.

There is a conjugate axis through the center which is 2b units long.

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m = ±ba

or ±ab

There are two asymptotes through the centerwith slopes