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The locus of the image of a variable point ( , 2 -1) with respect to the line 3 x-2 y+4=0 , is

Options

  1. A22(13 x+36)=19(13 y-11)
  2. B30(13 x+36)=19(13 y+37)
  3. C22(13 x+36)=7(13 y+11)
  4. D22(13 x-36)=30(13 y-11)

Correct answer

A. 22(13 x+36)=19(13 y-11)

Step-by-step solution

Given a point P ( , 2 -1) with respect to the line 3 x-2 y+4=0 . Formula for locus of point p is x - x ₁ a = y - y ₁ ~b = -2 ( ax ₁+ by ₁+ c ) a ^2+ b ^2 Here, x ₁= , y ₁=2 -1, a =3, ~b =-2, c =4 aligned & x - 3 = y - z +1 -2 = -2(3( )+(-2)(2 -1)+4 3^2+2^2 & x - 3 = y - z +1 -2 = -2 13 (- +6) aligned compare variable terms with constant term aligned & x - 3 = -12 13 (- +6) & 13 x -13 =-6(- +6) & 13 x -13 =6 +36 & 13 x +36=19 aligned Now, aligned & y -2 +1 -2 = -2 13 (- +6) & 13 y -26 +13=4(- +6) & 13 y -26 +13+4 -2

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