Conics Parabolas, Hyperbolas and Ellipses Objective: Students will be able to apply past knowledge to solve equations fro parabolas. Students will be able to solve real world situations.

What do you remember Vertex Zeros Standard form Vertex form Factored form Complete the square Write equation given vertex and a point

New Parts to Parabola Focus point inside the parabola, on the axis of sym Directrix line outside the parabola, perpendicular to axis of sym Help in the formation of the parabola Focal Length –distance from vertex to focus or directrix this is p and is the same in both directions (focal length) Distance from Focus to a point on the parabola is equal to the distance from point to directrix (perpendicular) Focal with – through the focus, perpendicular to the axis of symm and touching 2 points on parabola

When p=1 you have the parent function of the parabola

Look at the distribution of the p value and the k value

When doing problems What is given What do we need to find Is it vertical or horizontal What is the general equation for the parabola Vertex? Focus? Directrix?

Homework Page 641 7-10 11,13,15,17,49,53,60

Ellipses Think of as a squished circle Set of all points P in the Plane such that the sum of the distances from P to the two fixed points F1 and F2, the two foci, is a constant Center of Ellipse is the midpoint joining the foci Foci – 2 fixed points Focal Axis – line through the Foci Vertices – where graph intersects axis

More With Ellipses Major Axis – chord that passes through the foci longest chord Endpoints are vertices of ellipse Minor Axis – chord that passes through the center and is perpendicular to the major chord shorter of the two axis endpoint are on the ellipse Ellipse is symmetric in regaurds to the major and minor axis

More Notes Ellipse Center to endpoint of major is a Full length of major is 2a Center to endpoint of minor is b Full length of minor is 2b De[pending on which fraction the larger number is under tells you the direction of the ellipse Center to foci is c General Equation

Standard form Can be horizontal or vertical – with center at origin, how would this change if center not origin