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Let the point A lies on 3 x - 4 y+ 1 = 0 , the point B lies on 4 x + 3 y - 7 = 0 and the point C is - 2,5 . If A B C D is a rhombus, then the locus of D is

Options

  1. A25 x + 2 2 + y - 5 2 = 3 x - 4 y + 1 2
  2. B3 x - 4 y + 1 2 + 4 x + 3 y - 7 2 = 1
  3. C3 x - 4 y + 1 2 - 4 x + 3 y - 7 2 = 1
  4. D4 x + 3 y - 7 2 - 3 x - 4 y + 1 2 = 1

Correct answer

A. 25 x + 2 2 + y - 5 2 = 3 x - 4 y + 1 2

Step-by-step solution

C - 2,5 lies on 4 x + 3 y - 7 = 0 ⇒ B C is perpendicular to 3 x - 4 y + 1 = 0 ⇒ D A is perpendicular to 3 x - 4 y + 1 = 0 ⇒ Because D A = D C so, the distance of D from 3 x - 4 y + 1 = 0 is equal to D C ⇒ h + 2 2 + k - 5 2 = 3 h - 4 k + 1 5 ⇒ 25 x + 2 2 + y - 5 2 = 3 x - 4 y + 1 2

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