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AP EAMCET2003MathematicsEllipse

The eccentricity of the ellipse 9 x^2+5 y^2-18 x-20 y-16=0 , is :

Options

  1. A1 2
  2. B2 3
  3. C3 2
  4. D2

Correct answer

B. 2 3

Step-by-step solution

Equation of ellipse is 9 x^2+5 y^2-18 x-20 y-16=0 9 (x^2-2 x )+5 (y^2-4 y )=16 9 (x^2-2 x+1 )+5 (y^2-4 y+4 )=16+9+20 9(x-1)^2+5(y-2)^2=45 (x-1)^2 5 + (y-2)^2 9 =1 Here a^2=5, b^2=9 eccentricity, e= 1- a^2 b^2 = 1- 5 9 = 2 3

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