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This question is public and is used in 1 group and 11 tests or worksheets.

Type: Multiple-Choice
Category: Nonlinear Equations and Functions
Level: Grade 11
Standards: HSG-GPE.A.3
Author: nsharp1
Created: 6 years ago

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Nonlinear Equations and Functions Question

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For the ellipse with foci F1=(-c,0) and F2=(c,0), derive the equation of the ellipse.

Grade 11 Nonlinear Equations and Functions CCSS: HSG-GPE.A.3

Substituting the equations for d1,d2 found in the second and third questions into the above equation, and then moving the second square root term to the right side of the equation results in the following:
√(x+c)2+y2=2a-√(x-c)2+y2
The next step will be to square both sides. Why was the second square root term moved to the right side of the equation before squaring, instead of just squaring both sides immediately?
  1. It gets rid of all square root terms immediately.
  2. It will make the algebra easier later on, since the two square root terms are not multiplied together.
  3. This ensures that there won't be any multiple answers that usually result from square roots (taking the positive and negative).
  4. This makes that equation more balanced, which looks nicer.