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in Co-ordinate geometry by (52.7k points)

Find the equation of the locus of a point so that the sum of its distance from two given points P(3, 2) and Q(4, 3) is 4.

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Let the required variable point be R(h, k). We have PR + QR = 4;  hence

h2 + k2 + 196 - 28h - 28k + 2hk = 16h2 + 16k2 + 400 - 96k

⇒  15h2 + 15k2 - 2hk - 100h - 68 + 204 = 0

Squaring both the sides, we have

Hence, the locus is 

152 + 15y2 - 2xy -100x - 68y + 204 = 0 

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