ELLIPSE A stretched circle An ellipse is a

ELLIPSE A stretched circle

An ellipse is a geometric locus: of points having a common characteristic. set

Graphing an ellipse on a graphing calculator: STEPS: 1) Isolate y 2 2) Square Root both sides 3) Graph: y = +√ y = -√

Example: 1) Draw the ellipse on a Cartesian Plane 2) Is the MAJOR axis horizontal or vertical? 3) Find the coordinates of the vertices 4) Find the coordinates of the FOCI 5) Find the length of the major axis 6) Find the length of the minor axis

Example: Find the equation of the ellipse

Example: Find the coordinates of the foci of an ellipse centered at the origin, whose vertices have the coordinates: (8, 0) and (0, -4)

Equation of the Ellipse in GENERAL Form ax 2 + by 2 + c = 0 Ellipse: From STANDARD to GENERAL ax 2 + by 2 + c = 0 Ex. 1: Write the following equation in GENERAL form: STEPS: 1) Find COMMON DENOMINATOR 2) Multiply both sides by the common denominator 3) Make equation = to 0 Ex. 2: Write the following equation in GENERAL form:

Ellipse: From GENERAL to STANDARD ax 2 + by 2 + c = 0 Ex. 1: Write the following equation in STANDARD form: STEPS: 1) Transfer the opposite of "c" to the other side 2) Divide both sides by the opposite of "c" (to make the right side = to 1) 3) Simplify the coefficients of x 2 & y 2 to 1 number

Graphing Inequalities: ELLIPSES EX: Determine the rule of the following inequality:

System of Inequalities EX: Determine the system of inequalities: 1) Find the inequality of the ELLIPSE: 2) Find the inequality of the LINE:

Points of Intersection between a Line & an Ellipse