The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils determine what happens to the graph as they translate the point horizontally and vertically.

Concepts

circles, equation of a circle, slope, tangent, tangent lines, point-slope form

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Additional Tags

math

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Instructional Ideas

• Create a diagram of the situation in a dynamic geometry software that helps class members manipulate the scenario

Classroom Considerations

• Individuals should be able to graph a circle given the equation
• Expects the class understands tangents to a circle

Pros

• Answer key contains the required solution graph along with a description
• Illustration of the initial setup of the problem in the answer key helps students start on the right foot
  

Cons

• None

Common Core

HSA-REI.C.7 HSG-C.A.2 HSG-C.A.4 MP1