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AP EAMCET202318 May 2023Morning ShiftMathematicsStraight LinesActual

If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point P such that PA + PB =8 is

Options

  1. A16 x^2+7 y^2-64 x-48=0
  2. B16 x^2+7 y^2-64 x+48=0
  3. C16 x^2-7 y^2+64 x-48=0
  4. D16 x^2-7 y^2+64 x+48=0

Correct answer

A. 16 x^2+7 y^2-64 x-48=0

Step-by-step solution

Let co-ordinate of point P is ( x , y ) Now, PA + PB =8 aligned & (x-2)^2+(y-3)^2 + (x-2)^2+(y+3)^2 =8 & (x-2)^2+(y-3)^2 =8- (x-2)^2+(y+3)^2 & (x-2)^2+(y-3)^2=64+(x-2)^2+(y+3)^2 & -16 (x-2)^2+(y+3)^2 & 4 (x-2)^2+(y+3)^2 =16+3 y & 16 (x^2+4-4 x+y^2+9+6 y )=256+9 y^2+96 y & 16 x^2+7 y^2-64 x-48=0 aligned

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