What do a line and an ellipse have in common? Maybe zero, one, or two points! Learners consider the equation of an ellipse and a line to determine if their graphs have any shared points. They then write a system of equations, including both an ellipse and line, that have either two or no points in common.

Concepts

ellipses, linear equations, graphing conic sections, conic sections, systems of equations, nonlinear systems

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Additional Tags

math

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Instructional Ideas

• Repeat the task with the equation of a hyperbola and a line
• Use graphing calculators or similar online technology to check solutions graphically

Classroom Considerations

• Expects a solid understanding of graphing ellipses

Pros

• Presents an open-ended question with multiple solution methods
• Provides the resources in an editable format

Cons

• None

Common Core

HSG-GPE.A.3