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AP EAMCET202017 Sep 2020Morning ShiftMathematicsEllipseActual

Foci of the ellipse (2 x^2+3 y^2-4 x-12 y+13=0 ) are

Options

  1. A( (1+ 1 6 , 2 ) ) and ( (1- 1 6 , 2 ) )
  2. B( ( 1 6 +1,2 ) ) and ( ( 1 6 -1,2 ) )
  3. C( (2,1+ 1 6 ) ) and ( (2,1- 1 6 ) )
  4. D( (2, 1 6 +1 ) ) and ( (2, 1 6 -1 ) )

Correct answer

A. ( (1+ 1 6 , 2 ) ) and ( (1- 1 6 , 2 ) )

Step-by-step solution

Given ellipse ( array rlrl & & 2 x^2+3 y^2-4 x-12 y+13 & =0 & 2(x-1)^2+3(y-2)^2 & =1 & & (x-1)^2 ( 1 2 )^2 + (y-2)^2 ( 1 3 )^2 & =1 array ) ( aligned & e= 1- b^2 a^2 = 1- 1 / 3 1 / 2 = 1 3 & a= 1 2 , b= 1 3 a e= 1 6 aligned ) Foci ( (h a e, k)= (1 1 6 , 2 ) )

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