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AP EAMCET202316 May 2023Evening ShiftMathematicsStraight LinesActual

If the equations x = t ^2+ t +1, y = t ^2- t +1 represents a curve C with parameter t , then the Cartesian equation of C is

Options

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

Correct answer

A. x^2-2 x y+y^2-2 x-2 y+4=0

Step-by-step solution

Given x = t ^2+ t +1, y = t ^2- t +1 Now, x+y=2 (t^2+1 ) ... (i) x - y =2 t ... (ii) From (i) & (ii), we get aligned & x+y=2 [1+ ( x-y 2 )^2 ] & x+y= ( 4+x^2+y^2-2 x y 2 ) & x^2+y^2-2 x-2 y-2 x y+4=0 aligned

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