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AP EAMCET201822 Apr 2018Evening ShiftMathematicsStraight LinesActual

When the origin is shifted to the point (2,3) and then the coordinate axes are rotated through an angle 3 in the counter clockwise sense, then the transformed equation of 3 x^2+2 x y+3 y^2-18 x-22 y+50=0 is

Options

  1. A3 x^2+3 y^2-1=0
  2. B(6+ 3 ) x^2-2 x y+(6- 3 ) y^2-2=0
  3. C4 x^2+2 y^2-1=0
  4. D(6- 3 ) x^2+(6+ 3 ) y^2+2 x y=0

Correct answer

B. (6+ 3 ) x^2-2 x y+(6- 3 ) y^2-2=0

Step-by-step solution

We first change the origin, by putting x^ +2 and y^ +2 for x and y respectively. The new equation will be gathered 3 (x^ +2 )^2+2 (x^ +2 ) (y^ +3 )+3 (y^ +3 )^2- 18 (x^ +2 )-22 (y^ +3 )+50=0 gathered It reduces to Dropping the suffices, we get the equation 3 x^2+2 x y+3 y^2-1=0 To turn the axes through an angle of 3 , in the counter clockwise sense, we must write x^ - 3 y^ 2 for x and 3 x^ +y^ 2 for y . The Eq. (i) will then be aligned & 3 ( x^ - 3 y^ 2 )^2+2 ( x^ - 3 y^ 2 ) ( 3 x^ +y^ 2 )+ & 3 ( 3 x^ +y^ 2 )^2-1=0

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