EAMCET Engineering 2005 Solved Paper

Since the line y−3x=0 touches the circle
∴ radius = perpendicular distance from the centre (1,1) to the tangent
=‌

|1−3|

√1+9

=‌

2

√10

. . . (i)
Let the other equation of tangent which is passing through origin is y=mx.
‌ radius ‌=‌

|1−m|

√1+m2

⇒‌

4

10

=‌

(1−m)2

(1+m2)

⇒2(1+m2)=5(1+m2−2m)
⇒3m2−10m+3=0
⇒3m2−9m−m+3=0
⇒(3m−1)(m−3)=0
⇒m=3,‌

1

3

at m=3,y=3x it is already given.
at m=‌

1

3

,3y=x