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