Questions
The locus of midpoints of the perpendicular drawn from the points on the line to the line x=y is
detailed solution
Correct option is D
The general point on the line x=3y is 3h,hThe foot of the perpendicular of 3h,h on the line x=y is l,m l−3h1=m−h−1=−3h−h12+12 Simplify l−3h1=−h⇒l=2h And m−h−1=−h⇒m=2h Hence the foot of the perpendicular of 3h,h on the line x−y=0 is 2h,2hSuppose that Px1,y1 be any point on the locus.The point Px1,y1 is midpoint of 3h,h and 2h,2hIt implies that x1,y1=5h2,3h2Eliminate h to get the locus of the point Px1,y1 Therefore, the locus is 2x5=2y3⇒3x−5y=0Talk to our academic expert!
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