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AP EAMCET2004MathematicsEllipse

The eccentricity of the conic 36 x^2+144 y^2-36 x-96 y-119=0 is

Options

  1. A3 2
  2. B1 2
  3. C3 4
  4. D1 3

Correct answer

A. 3 2

Step-by-step solution

Given equation of conic is aligned & 36 x^2+144 y^2-36 x-96 y-119=0 & 36 (x^2-x )+144 (y^2- 2 3 )=119 & 36 (x^2-x+ 1 4 )+144 (y^2- 2 3 + 1 9 ) & =119+9+16 & 36 (x- 1 2 )^2+144 (y- 1 3 )^2=114 & (x- 1 2 )^2 4 + (y- 1 3 )^2 1 =1 & aligned This is the equation of ellipse. Here, e= 1- b^2 a^2 = 1- 1 4 = 3 2

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