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AP EAMCET201823 Apr 2018Evening ShiftMathematicsStraight LinesActual

The transformed equation of 3 x^2-6 x y+8 y^2=8 when the axes are rotated about the origin through an angle 4 in the positive direction, is

Options

  1. A5 x^2+10 x y+17 y^2+16=0
  2. B5 x^2+10 x y+17 y^2-16=0
  3. C5 x^2-10 x y+17 y^2-16=0
  4. D5 x^2-10 x y+17 y^2+16=0

Correct answer

B. 5 x^2+10 x y+17 y^2-16=0

Step-by-step solution

Given transformed equation is 3 x^2-6 x y+8 y^2=8 Now, x^ =x 4 -y 4 = x-y 2 and y^ =x 4 +y 4 = x+y 2 Before transformation the equation is aligned & 3 ( x-y 2 )^2-6 ( x-y 2 ) ( x+y 2 )+8 ( x+y 2 )^2=8 & 3 (x^2+y^2-2 x y )-6 (x^2-y^2 ) & +8 (x^2+y^2+2 x y )=16 & 5 x^2+17 y^2+10 x y-16=0 . aligned

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