KKhaemenes PrecalculusTeacher Answer Key
Student Lesson

Teacher Key · Unit 11 · Lesson 05

Ellipses and Their Geometry

Use this key to verify method, notation, domain, units, and interpretation. Accept equivalent exact forms when mathematically valid.

Khaemenes Academy · Teacher Key

Ellipses and Their Geometry

U11 · L05
1

Identify (x−2)²=8(y+1).

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: Parabola opening upward
Reasoning: 4p=8>0 with vertical axis.
2

Find the center of (x+3)²/16+(y−2)²/9=1.

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: (−3,2)
Reasoning: Read h and k from translated form.
3

Find the semi-major axis of x²/25+y²/9=1.

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: 5
Reasoning: The larger denominator is 25.
4

Identify x²/9−y²/4=1.

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: Horizontal hyperbola
Reasoning: Opposite signs and positive x-term.
5

State the asymptotes of x²/9−y²/4=1.

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: y=±(2/3)x
Reasoning: Use y=±(b/a)x.
6

For y²=12x, find p.

Conics visualRecognize, graph, and model parabolas, ellipses, and hyperbolas from standard, translated, and contextual forms. xy
Answer: 3
Reasoning: 4p=12.
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