Points A and B respectively lie on positive X-axis & positive Y-axis and point C lies in first quadrant such that AB, BC, CA are in ratio 5 : 4 : 3 respectively, locus of point C is (when A moves on X, B moves on Y.)
(A) 3x = 4y                    (B) y = 2x                   (C) x = 3y                  (D) None

Hi, Take A a,0 and B0,b and C h,know since AB:BC:CA = 5:4:3so let AB = 5k and BC= 4k and AC = 3k so Here we can see that, AB2= BC2+AC225k2= 16k2+9k2so AB, BC, CA are following pythagorus theorem and ABis hypotenuseand C is the fixed point with angle 90 degreeso product of slopes of AC and BCwill result in -1 so k-0h-a×k-bh-0  = -1k2-kb = -h2+ahh2+k2-ah-kb = 0 so it will be a circle so D is the answer

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