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Let D is a point on the line l 1 : x + y - 2 = 0 and S 3,3 is a fixed point. The line l 2 is perpendicular to D S and passes through S . If M is another point on the line l 1 (other than D ), then the locus of the point of intersection of l 2 and the angle bisector of the angle M D S is

Options

  1. Ax + y - 2 2 = 2 x - 3 2 + 2 y - 3 2
  2. Bx + y - 2 2 = x - 3 2 + y - 3 2
  3. Cx + y - 2 2 = x - 3 2 + y - 3 2 2
  4. DNone of these

Correct answer

A. x + y - 2 2 = 2 x - 3 2 + 2 y - 3 2

Step-by-step solution

Let the point of intersection of l 2 and the angle bisector of angle M D S is P h , k . Draw perpendicular P F to l 1 from P . Now, ∆ P F D & ∆ P S D are congruent triangles. Hence, P F = P S h + k - 2 2 = h - 3 2 + k - 3 2 ⇒ x + y - 2 2 = 2 x - 3 2 + y - 3 2

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