Lesson Worksheet: Eccentricity of Conic Sections Mathematics • 12th Grade

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 (π‘₯βˆ’β„Ž)π‘Žβˆ’(π‘¦βˆ’π‘˜)𝑏=1.

  • Aβˆšπ‘Ž+π‘οŠ¨οŠ¨
  • Bβˆšπ‘Žβˆ’π‘π‘ŽοŠ¨οŠ¨
  • Cβˆšπ‘Ž+π‘π‘ŽοŠ¨οŠ¨
  • Dπ‘Ž+π‘π‘ŽοŠ¨οŠ¨

Q2:

Calculate the eccentricity of the hyperbola with the equation (π‘₯+1)3βˆ’(π‘¦βˆ’2)9=1.

Q3:

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

  • A0
  • B0.6
  • Cβˆ’0.3
  • D1.5
  • E1

Q4:

Calculate the eccentricity of the hyperbola with equation 4π‘¦βˆ’5π‘₯βˆ’24π‘¦βˆ’20π‘₯=4.

  • A3√5
  • B9√5
  • C32
  • D3

Q5:

Calculate the eccentricity of an ellipse with the equation (π‘₯βˆ’1)5+(π‘¦βˆ’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 (π‘₯βˆ’β„Ž)π‘Ž+(π‘¦βˆ’π‘˜)𝑏=1.

  • A𝑒=βˆšπ‘Ž+π‘π‘ŽοŠ¨οŠ¨
  • B𝑒=βˆšβ„Žβˆ’π‘˜οŠ¨οŠ¨
  • C𝑒=βˆšπ‘Žβˆ’π‘π‘ŽοŠ¨οŠ¨
  • D𝑒=βˆšπ‘Žβˆ’π‘οŠ¨οŠ¨
  • E𝑒=βˆšβ„Žβˆ’π‘˜β„ŽοŠ¨οŠ¨

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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