# Activities

• • • ##### Subject Area

• Math: Algebra II: Conics

• ##### Author 9-12

45 Minutes

Derive™ 6

• ##### Report an Issue

Equations for Curves Passing through a Given Set of Points

#### Activity Overview

In this Derive™ activity, students explore equations of curves which pass through a set of given points. They use this method to determine the location of a distribution center which is equidistant from the outlets of a large department store chain.

#### Before the Activity

• See the attached DFW file for detailed instructions for this activity
• Print pages from the attached DFW file for your class
• #### During the Activity

Distribute the pages to the class.

• Set up a 2D plot window
• Use 3 random locations on the coordinate system
• Simplify the expression and assign result to the variable loc
• Guess the best location for the center of a circle which encompasses the 3 points
• Substitute guesses for the center and radius of the circle in the equation for the center of a circle and plot the result
• Expand the equation of the circle
• Simplify the given expression to see the three unknown equations
• Solve for the radius, and the coordinates of the center

• Extend the procedure to find a curve that passes through a given number of points by considering the equation for a parabola
• Generate three points at random and assign the result to a variable
• Plot the three points
• Substitute these three points into the equation of the parabola to obtain three equations in the three unknowns
• Solve the equations for the unknowns and plot the parabola
• #### After the Activity

Students answer questions listed on the activity sheet.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary