The locus of the mid-points of the perpendiculars drawn from points on the line, x=2y to the line x=y is :
A
2x−3y=0
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B
3x−2y=0
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C
5x−7y=0
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D
7x−5y=0
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Solution
The correct option is C5x−7y=0
Let R be the mid-point of PQ whose locus is (h,k) PQ is perpendicular to line y=x ∴ Equation of the line PQ can be written as y=−x+c y=−x+c intersects y=x at Q(c2,c2) y=−x+c intersects x=2y at P(2c3,c3) ∴ Coordinates of midpoint isR(7c12,5c12)
Locus of R:h=7c12,k=5c12 ⇒5h−7k=0 ∴ locus of required equation is 5x−7y=0