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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 hyperbola centered at the origin with foci F1=(-c,0) and F2=(c,0), derive the equation of the hyperbola.

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

Substitute the equations for d1,d2 found in the second and third questions into the equation in the previous question. After some rearranging, the result is the following equation:

√(x+c)2+y2=±2a+√(x-c)2+y2

Why is there a plus-minus sign on the 2a term?
  1. In order to remove the absolute value sign, one has to consider the case where d1>d2 and d1<d2.
  2. To remove the square root from this term, one has to look at the positive and negative case.
  3. Since it's not certain which side of the equation this term should be on, it could be either positive or negative.
  4. This is a hyperbola and the curves can be on either the positive or negative x-axis.