Locus:
The equation to a locus is relation which exists between coordinates of any point on the path, and which holds for no other point except those lying on path.
Working rule to find the locus of a point:
Step 1: Let coordinates of the moving point be P(h, k).
Step 2: Write down the given geometrical condition and express these conditions in the terms of h and k.
Step 3: Eliminate variable to get the relation in h and k that is. this relation should contain only h, k and known as quantities.
Step 4: Express the given relation in h and k in simplest form and then put x for h and y for k. The relation obtained, will be the required equation of locus of P(h, k).
Illustration: Find locus of a point P which divides line joining (1, 0) and (2 cosq, 2 sinq) internally in the ratio 2 : 3 for all q.
Solution: Let coordinate of point P which divides line joining (1, 0) and (2cosq, 2sinq) in the ratio 2 : 3 be (h, k) then
= (5h-3)2 + (5k)2 = 16
Thus the locus is (5x - 3)2 + (5y)2 = 16
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