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The eccentricity of the ellipse 9x2 + 5y2 – 30y = 0 is:
  • a)
    1/3
  • b)
    2/3
  • c)
    3/4
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The eccentricity of the ellipse 9x2+ 5y2– 30y = 0 is:a)1/3b)2/3c...
9x2 + 5y2 - 30y = 0
9x2 + 5(y−3)2 = 45
We can write it as : [(x-0)2]/5 + [(y-3)2]/9 = 1
Compare it with x2/a2 + y2/b2 = 1
e = [(b2 - a2)/b2]½
e = [(9-5)/9]1/2
e = (4/9)½
e = ⅔
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Community Answer
The eccentricity of the ellipse 9x2+ 5y2– 30y = 0 is:a)1/3b)2/3c...
To find the eccentricity of the ellipse, we need to first put the given equation in the standard form of an ellipse, which is:

(x^2/a^2) + (y^2/b^2) = 1

where 'a' and 'b' are the semi-major and semi-minor axes of the ellipse, respectively.

1. Rearrange the equation:
9x^2 + 5y^2 + 30y = 0

2. Complete the square for the y terms:
9x^2 + 5(y^2 + 6y) = 0

3. Divide the coefficient of x^2 by the constant term to determine 'a':
a^2 = -30/9
a^2 = -10/3
a = sqrt(-10/3) (imaginary)

4. Divide the coefficient of y^2 by the constant term to determine 'b':
b^2 = -5/9
b = sqrt(-5/9) (imaginary)

Since 'a' and 'b' are imaginary, this means that the given equation does not represent a real ellipse, but rather a degenerate ellipse or a pair of intersecting lines.

5. Calculate the eccentricity (e):
The eccentricity of an ellipse is defined as the square root of (1 - (b^2/a^2)).

e = sqrt(1 - (b^2/a^2))
e = sqrt(1 - (-5/9) / (-10/3))
e = sqrt(1 + 5/6)
e = sqrt(11/6)

Therefore, the eccentricity of the given ellipse is sqrt(11/6), which is approximately 0.8819. None of the given options (a, b, c, d) match this value, so the correct answer is None of these.
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The eccentricity of the ellipse 9x2+ 5y2– 30y = 0 is:a)1/3b)2/3c)3/4d)None of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The eccentricity of the ellipse 9x2+ 5y2– 30y = 0 is:a)1/3b)2/3c)3/4d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The eccentricity of the ellipse 9x2+ 5y2– 30y = 0 is:a)1/3b)2/3c)3/4d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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