Derive conic equations

Start lessonBegins with Derive ellipse equation · Slides

Teacher tools for this standard

Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSG.GPE.A.3

**HSG.GPE.A.3**: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

HSG.GPE.A.3: (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

What you'll learn

Define an ellipse as the locus of points where the sum of distances from two foci equals a constant 2a, and derive the standard equation x^2/a^2 + y^2/b^2 = 1 where b^2 = a^2 - c^2
Define a hyperbola as the locus of points where the absolute difference of distances from two foci equals a constant 2a, and derive the standard equation x^2/a^2 - y^2/b^2 = 1 where b^2 = c^2 - a^2
Identify the key features of ellipses and hyperbolas from their equations: center, vertices, foci, axes, and (for hyperbolas) asymptotes
Compute the eccentricity of an ellipse or hyperbola and explain how it describes the shape
Distinguish between ellipses and hyperbolas based on their equations and geometric definitions

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