Manipal Entrance Test 2020 Math Paper

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, 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
On putting the values of m=−1 and c=±√2 in Eq. (i), we get
y=−x±√2