Expressing Geometric Properties with Equations
PrintExpressing 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.
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.
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?
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?
What is its center?

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