Let D is a point on the line l 1 : x + y - 2 = 0 , S 3 , 3 is a fixed point and line l 2 is the perpendicular to D S and passing through S . If M K is another point on the line l 1 (other than D ), then the locus of the point of intersection of l 2 and angle bisector of the angle M D S is a conic whose length of latus rectus rectum is equal to

Question

Let D is a point on the line l 1 : x + y - 2 = 0 , S 3 , 3 is a fixed point and line l 2 is the perpendicular to D S and passing through S . If M K is another point on the line l 1 (other than D ), then the locus of the point of intersection of l 2 and angle bisector of the angle M D S is a conic whose length of latus rectus rectum is equal to, 4 2, 4, 8, 2 2

MARKS App · Accepted Answer

Let the point of intersection of l 2 and angle bisector of the angle M D S is P h , k . Draw perpendicular P F to l 1 from P . Now, Δ P F D and Δ P S D are congruent triangles. Hence, P F = P S ⇒ locus of P is a parabola having S as focus and l 1 as the directrix Hence, the length of the latus rectum is 2 3 + 3 - 2 1 + 1 = 4 2 units

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