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AP EAMCET202421 May 2024Morning ShiftMathematicsCircleActual

When the origin is shifted to (h, k) by translation of axes, the transformed equation of x^2+2 x+2 y-7=0 does not contain x term and constant term. Then (2 h+k)=

Options

  1. A7 2
  2. B1 2
  3. C2
  4. D0

Correct answer

C. 2

Step-by-step solution

aligned & X +h=x, Y +k=y & ( X +h)^2+2( X +h)+2( Y +k)-7=0 & X ^2+(2 h+2) X +2 Y +h^2+2 h+2 k-7=0 aligned To remove X - term, 2 h+2=0 h=-1 To remove constant term, h^2+2 h+2 k-7=0 1-2+2 k-7=0 k=4 2 h+k=-2+4=2

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