Lesson Worksheet: Eccentricity of Conic Sections Mathematics

In this worksheet, we will practice finding the eccentricity of conic sections and using it to find their equations or types.

Q1:

Give the formula for the eccentricity of the hyperbola with equation (𝑥−ℎ)𝑎−(𝑦−𝑘)𝑏=1.

  • A√𝑎+𝑏
  • B√𝑎−𝑏𝑎
  • C√𝑎+𝑏𝑎
  • D𝑎+𝑏𝑎

Q2:

Calculate the eccentricity of the hyperbola with the equation (𝑥+1)3−(𝑦−2)9=1.

Q3:

Which of the following could be the eccentricity of a hyperbola?

  • A0
  • B0.6
  • C−0.3
  • D1.5
  • E1

Q4:

Calculate the eccentricity of the hyperbola with equation 4𝑦−5𝑥−24𝑦−20𝑥=4.

  • A3√5
  • B9√5
  • C32
  • D3

Q5:

Calculate the eccentricity of an ellipse with the equation (𝑥−1)5+(𝑦−2)3=1.

  • A√105
  • B√25
  • C√102
  • D2√105
  • E√63

Q6:

Which of the following could be the eccentricity of an ellipse?

  • A1.3
  • B0
  • C1
  • D0.6

Q7:

Which of the following represents the eccentricity of an ellipse?

  • A𝑒<0
  • B𝑒=0
  • C0<𝑒<1
  • D𝑒>1
  • E𝑒=1

Q8:

Give the formula for the eccentricity of the ellipse with the equation (𝑥−ℎ)𝑎+(𝑦−𝑘)𝑏=1.

  • A𝑒=√𝑎+𝑏𝑎
  • B𝑒=√ℎ−𝑘
  • C𝑒=√𝑎−𝑏𝑎
  • D𝑒=√𝑎−𝑏
  • E𝑒=√ℎ−𝑘ℎ

Q9:

Which of the following represents the eccentricity of a hyperbola?

  • A0<𝑒<1
  • B𝑒>1
  • C0≤𝑒≤1
  • D𝑒=0
  • E𝑒=1

Q10:

Which of the following represents the eccentricity of a parabola?

  • A0<𝑒<1
  • B0≤𝑒≤1
  • C𝑒=1
  • D𝑒=0
  • E𝑒>1

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