HOTS : Straight Line

Prob 1.  Two points A and B move on the +ve direction of x-axis and y-axis respectively, such that OA + OB = a. Show that the locus of the foot of the perpendicular from the origin O on the line AB is (x + y)(x2 + y2) = axy.

Sol.

Let the equation of AB be

….(1)

given,  a + b = α           ….(2)

now, mAB × mOM = -1

⇒  ah = bk                    ….(3)

from (2) and (3),

∴  from (1)

as it passes through (h , k)

⇒ (h + k) (h2 + k2) = αhk

∴ locus of (h , k) is (x + y) (x^2 + y^2) = αxy.

Next Page »