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AP EAMCET202318 May 2023Morning ShiftMathematicsStraight LinesActual

The transformed equation of 2 x^2+3 y^2-z^2-8 x+18 y+2 z+9=0 when the axes are translated to the point (2,-3,1) is

Options

  1. A2 x^2+3 y^2-z^2=25
  2. B2 x^2+3 y^2+z^2=25
  3. C2 x^2-3 y^2-z^2=25
  4. D2 x^2+3 y^2-z^2=50

Correct answer

A. 2 x^2+3 y^2-z^2=25

Step-by-step solution

Since the axes are translated by (2,-3,1) aligned & Let x-2=X x=X+2 & y+3=Y y=Y-3 & z-1=Z z=Z+1 aligned 2 x^2+3 y^2-z^2-8 x+18 y+2 z+9=0 array ll & 2( X +2)^2+3( Y -3)^2-( Z +1)^2-8( X +2)+18 & ( Y -3)+2( Z +1)+9=0 & 2 ( X ^2+4+4 X )+3 ( Y ^2+9-6 Y )- ( Z ^2+1+2 Z ) & -8 X -16+18 Y -54+2 Z +2+9=0 & 2 X ^2+3 Y ^2- Z ^2=25 array

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