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[A-REI8]
Conic Sections
Understand the graphs and equations of conic sections.
15.
Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate
conics, from second-degree equations.
Example:
Graph
x
2
– 6
x
+
y
2
– 12
y
+ 41 = 0 or
y
2
– 4
x
+ 2
y
+ 5 = 0.
a.
Formulate equations of conic sections from their determining characteristics.
Example:
Write the equation of an ellipse with center (5, -3), a horizontal major axis
of length 10, and a minor axis of length 4.
Answer:
2
2
(
5)
(
3)
1.
25
4
x
y
−
+
+
=

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