CGPET 2014 Solved 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, 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