Let P=(h,k) Now, according to the question, ‌‌
√(h−1)2+(k−1)2
|‌
h−k+2
√12+(−1)2
|
=‌
1
√2
‌⇒‌
2[(h−1)2+(k−1)2]
(h−k+2)2
=‌
1
2
[squaring both sides] ⇒4[(h2−2h+1)+(k2−2k+1)] ‌=h2+k2+4−2hk−4k+4h ⇒3h2+2hk+3k2−12h−4k+4=0 ∴ The equation of the locus of P is 3x2+2xy+3y2−12x−4y+4=0