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AP EAMCET2009MathematicsStraight Lines

The transformed equation of x^2+y^2=r^2 when the axes are rotated through an angle 36^ is

Options

  1. A5 X^2-4 X Y+Y^2=r^2
  2. BX^2+2 X Y- 5 Y^2=r^2
  3. CX^2-Y^2=r^2
  4. DX^2+Y^2=r^2

Correct answer

D. X^2+Y^2=r^2

Step-by-step solution

Given equation is x^2+y^2=r^2 . After rotation aligned & x=X 36^ -Y 36^ & and y=X 36^ +Y 36^ & X^2 ( ^2 36^ + ^2 36^ ) & & Y^2 ( ^2 36^ + ^2 36^ )=r^2 & X^2+Y^2=r^2 aligned

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