Worksheet: Equation of an Ellipse

In this worksheet, we will practice finding the equation of an ellipse using different givens and using it to solve problems that involve ellipse-shaped constructions.

Q1:

Derive the equation of an ellipse with foci at the points (1,3) and (6,3), which has a major axis of length 15.

  • A(2𝑥3)225+(𝑦7)50=1
  • B(2𝑥7)225+(𝑦3)50=1
  • C(2𝑥7)50+(𝑦3)225=1
  • D(𝑥7)225+(𝑦3)50=1
  • E(2𝑥3)50+(𝑦7)225=1

Q2:

An ellipse has a vertex at (11,5) and a covertex at (6,8). The major axis of the ellipse is parallel to the 𝑥-axis. What is the equation of the ellipse?

  • A𝑥25+𝑦9=1
  • B(𝑥6)25+(𝑦5)9=1
  • C(𝑥6)5+(𝑦5)3=1
  • D𝑥9+𝑦25=1
  • E(𝑥5)25+(𝑦6)9=1

Q3:

Derive the equation of an ellipse centered at the origin with foci at the points (4,0) and (4,0), which has a major axis of length 10.

  • A𝑥5+𝑦3=1
  • B𝑥25+𝑦9=1
  • C𝑥9+𝑦25=1
  • D𝑥16+𝑦25=1
  • E𝑥25+𝑦16=1

Q4:

Derive the equation of an ellipse centered at the origin with foci at the points (2,0) and (2,0), which has its vertices at the points (8,0) and (8,0).

  • A𝑥16+𝑦64=1
  • B𝑥48+𝑦16=1
  • C𝑥25+𝑦64=1
  • D𝑥64+𝑦60=1
  • E𝑥48+𝑦64=1

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