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The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricit

Practice Questions

Q1
The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?
  1. 0.5
  2. 0.6
  3. 0.7
  4. 0.8

Questions & Step-by-Step Solutions

The equation of an ellipse is given by 4x^2 + 9y^2 = 36. What is the eccentricity of the ellipse?
  • Step 1: Start with the given equation of the ellipse: 4x^2 + 9y^2 = 36.
  • Step 2: Divide the entire equation by 36 to simplify it: (4x^2)/36 + (9y^2)/36 = 1.
  • Step 3: This simplifies to x^2/9 + y^2/4 = 1.
  • Step 4: Identify a^2 and b^2 from the equation: a^2 = 9 and b^2 = 4.
  • Step 5: Calculate c using the formula c = √(a^2 - b^2): c = √(9 - 4) = √5.
  • Step 6: Find the eccentricity e using the formula e = c/a: e = √5/3.
  • Step 7: Approximate the value of e: e ≈ 0.6.
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