Let the equation of tangent be y=mx+c . . . (i) Given equation of circle is x2+y2−2x−2y+1=0 Its centre is (1,1) and radius, r=√12+12−1=√1+1−1=1 We know that, if line y=mx+c be a tangent to the circle, then ‌c‌=±r√1+m2 ∴‌c‌=±1√1+m2 . . . (ii) Since, the tangent line is perpendicular to y=x. ∴‌m×1‌=−1‌(∵m1m2=−1) ⇒m‌=−1‌ On putting m=−1 in Eq. (ii), we get C‌=±1√1+(−1)2 ‌=±√1+1 ‌=±√2 On putting the values of m=−1 and c=±√2 in Eq. (i), we get y=−x±√2