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AP EAMCET201823 Apr 2018Morning ShiftMathematicsStraight LinesActual

When the coordinate axes are rotated by an angle ⁻¹ ( 3 4 ) about the origin, then the equation x^2+y^2=9 is transformed to the equation.

Options

  1. Ax^2-y^2=9
  2. Bx^2+y^2+2 x y=4
  3. Cx^2+y^2=9
  4. Dx^2-y^2+9=0

Correct answer

C. x^2+y^2=9

Step-by-step solution

When the coordinate axis rotated by are angle about origin, then aligned & x= x₁- y₁ and & y= x₁+ y₁ & Here, = ⁻¹ 3 4 aligned = 3 4 = 4 5 and = 3 5 So, x= 4 5 x₁- 3 5 y₁ and y= 3 5 x₁+ 4 5 y₁x and y satisfy the equation aligned & x^2+y^2=9 & ( 4 5 x₁- 3 5 y₁ )^2+ ( 3 5 x₁+ 4 5 y₁ )^2=9 aligned aligned & 16 25 x₁^2+ 9 25 y₁^2- 24 25 x₁ y₁ & + 9 25 x₁^2+ 16 25 y₁^2+ 24 25 x₁ y₁=9 & x₁^2+y₁^2=9 & aligned So, transformed equations is x^2+y^2=9

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