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AP EAMCET201824 Apr 2018Morning ShiftMathematicsStraight LinesActual

When the coordinate axes are rotated through an angle of 45^ about the origin in the positive direction, if the transformed equation of a curve is 17 x^2-16 x y+17 y^2=225 , then the original equation of that curve is

Options

  1. A25 x^2+9 y^2=225
  2. B9 x^2-25 y^2=225
  3. C25 x^2-16 x y+9 y^2=225
  4. D9 x^2+25 y^2=225

Correct answer

A. 25 x^2+9 y^2=225

Step-by-step solution

When the axes are rotated through 45^ about the origin in the positive direction then replace (x, y) by ( x 2 + y 2 , -x 2 + y 2 ) So, original equation of the curve, array r 17 ( x 2 + y 2 )^2-16 ( x 2 + y 2 ) ( -x 2 + y 2 ) +17 ( -x 2 + y 2 )^2=225 array aligned & 17 ( x^2 2 + y^2 2 +x y )-16 ( y^2 2 - x^2 2 ) & +17 ( x^2 2 + y^2 2 -x y )=225 & 17 x^2 2 +17 y^2 2 +17 x y-8 y^2+8 x^2 & +17 x^2 2 +17 y^2 2 -17 x y=225 & 17 x^2+17 y^2-8 y^2+8 x^2=225 & 25 x^2+9 y^2=225 aligned

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