Detailed investigation with extensive background notes for instructor and step by step outline for students to follow.
Students will be asked to use a slider to approximate the position of a tangent line of slope -1 to a circle centered at (0,0). The tangent line, x+y=k, requires use of a parameter.
Students will begin with a particular radius, 3, then solve a linear-quadratic system to determine the exact equation of one of the tangent lines. They will also be asked to enter an expression for the other tangent line of slope -1 using the same parameter k. After approximating the locations of similar tangent lines for other radii, they will be asked to solve a general system using radius r.
There are different systems offered to the instructor, depending on the sophistication of the student. Finally, a geometric solution is suggested using 45-45-90 triangles.
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Monday, May 5, 2014
Desmos Common Core Activity Linking Circles, Tangents and Linear-Quadr Systems
Posted by Dave Marain at 11:27 AM
Labels: algebra 2, circles, Common Core, Desmos, geometry, investigations, tangents
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