Chapter 9 By Caitlin Pellett Nate Shureb Conic

Chapter 9 By: Caitlin Pellett & Nate Shureb

Conic Section • Conic Section is when a plane intersects a double-napped cone. • It is the locus of a point p which moves in the plane of the focus f, and a fixed line d called the directrix.

• Video: http: //www. brightstorm. com/math/algebra 2/conic-sections/introduction-to-conic-sections/ • For more information: http: //mathworld. wolfram. com/Conic. Section. html • http: //math 2. org/math/algebra/conics. htm • http: //britton. disted. camosun. bc. ca/jbconics. htm

Parabola • The set of all points equidistant from a point, the focus, and a line, directrix. Focus lies on the axis of symmetry and the directrix is perpendicular to AOS. • P is the key; the distance from the vertex to the focus and directrix. • Standard form for parabolas are: – Vertical; x² = 4 py directrix y = -p; x = 0 – Horizontal; y² = 4 px directrix x = -p; y = 0

• Video: http: //www. brightstor m. com/math/algebra 2/quadratic-equationsandinequalities/introducti on-to-parabolas/ • Other Info: http: //www. mathwords. com/p/parabola. htm

Ellipse • Set of all points p in a plane, the sum of the distance between p and 2 fixed points, the foci, which is a constant. • The standard form for ellipse is: – x² / a² + y² / b² = 1 Major axis is horizontal, vertices (±a, 0) and co-vertices (0, ±b) – x² / b² + y² / a² = 1 Major axis is vertical, vertices (0, ±a) and co-vertices (±b, 0) • Foci: c² = a² - b²

• Video: http: //www. brightstorm. com/math/algebra-2/conic -sections/the-ellipse/ • More info: http: //www. algebralab. org/lessons/lesson. aspx? fil e=Algebra_conics_ellipse. xml

Circle • Set of all points (x, y) in a plane that are equidistant from the center of the circle. • The standard from for a circle is x² + y² = r² • R is the radius which is the distance from the center and any point (x, y) on the circle.

• Video: http: //www. brightstorm. com/math/algebra 2/conic-sections/the-circle/ • Extra Info: http: //www. algebralab. org/lessons/lesson. aspx ? file=Algebra_conics_circle. xml

Hyperbola • Set of all points p in a plane where the difference of the 2 fixed points is called the foci, is constant. • Standard Forms: – Horizontal; x² / a² - y² / b² =1 asymptote y = ±b / a; vertices (±a, 0) – Vertical; y² / a² – x² / b² = 1 asymptote y = ±a / b; vertices (0, ±a) • Foci: c² = a² + b²

• Video: http: //www. brightstorm. com/math/algebra 2/conic-sections/the-hyperbola/ • Extra Info: http: //math 2. org/math/algebra/conics. htm