G-GPE: Expressing Geometric Properties with Equations

Expressing Geometric Properties with Equations

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Expressing Geometric Properties with Equations connects coordinate algebra to geometry: one cluster derives equations of circles and parabolas from their geometric definitions, while a second uses coordinates to prove results about slopes, distances, midpoints, and partitioning of segments.

G-GPE.ATranslate between the geometric description and the equation for a conic sectionG-GPE.BUse coordinates to prove simple geometric theorems algebraically
Example Problems
What are the foci of the hyperbola represented by the equation
?
What is the distance between the following points?
and
Round your answer to the nearest hundredth, if necessary.
The parabola is reflected across the -axis.

What is the equation of the new parabola?
Point M is the midpoint of point A and point B. Find the coordinates of point B.


The equation of a circle is given below.


What is its center?
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