TS EAMCET 4 May 2018 Shift 1 Solved Paper

The chord y−mx−1=0 is tangent to the circle.
S1≡x2+y2−4x+1=0
‌Or,
(x−2)2+(y−0)2=3
Thus,

|2m+1|

√1+m2

=√3
4m2+1+4m=3+3m2
(m+2)2=6
m=−2±√6
The equation of chord is,
L=y+(2±√6)x−1=0
Let possible point is (x1,y1) for which chord L=0 is chord of contact of the circle.
So,
xx1+yy1−1=0
And,
y+(2±√6)x−1=0
Represent the same line.
Therefore,

x1

2±√6

=

y1

1

=

−1

1

(x1,y1)=(2±√6,1)