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.

Also written as G-GPE.3 or G.GPE.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.

Example Problems
What are the foci of the hyperbola represented by the equation
?
What are the foci of the hyperbola represented by the equation
?
The equation of an ellipse is given below.


What is its center?
Khan Academy Resources
Equation of a hyperbola from featuresCenter & radii of ellipses from equationVertices & direction of a hyperbolaEllipse standard equation & graphEquation of an ellipse from featuresGraph & features of ellipsesFoci of a hyperbola from equationFoci of an ellipse from equationFoci of an ellipse from radii
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