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AP EAMCET2011MathematicsEllipse

The eccentricity of the ellipse x^2+4 y^2+2 x+16 y+13=0 is

Options

  1. A3 2
  2. B1 2
  3. C1 3
  4. D1 2

Correct answer

A. 3 2

Step-by-step solution

Equation of ellipse x^2+4 y^2+2 x+16 y+13=0 array cc & (x^2+2 x )+ (4 y^2+16 y )+13=0 & (x^2+2 x+1 )+4 (y^2+4 y+4 )-16 & +13-1=0 & (x+1)^2+4(y+2)^2=4 & (x+1)^2 4 + (y+2)^2 1 =1 & X^2 4 + Y^2 1 =1 array where, X=x+1 and Y=y+2 Here, a^2=4 and b^2=1 i.e., a>b The eccentricity, array cc & b^2=a^2 (-e^2+1 ) & 1=4 (-e^2+1 )=-4 e^2+4 & e^2= 3 4 & e= 3 2 array

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