If y=3 x is a tangent to a circle with centre (1,1) , then the other tangent drawn through (0,0) to the circle is

Step-by-step solution

Since the line y-3 x=0 touches the circle radius = perpendicular distance from the centre (1,1) to the tangent Let the other equation of tangent which is passing through origin is y=m x . radius = |1-m| 1+m^2 aligned & 4 10 = (1-m)^2 (1+m^2 ) & 2 (1+m^2 )=5 (1+m^2-2 m ) & 3 m^2-10 m+3=0 & 3 m^2-9 m-m+3=0 & (3 m-1)(m-3)=0 & m=3, 1 3 aligned at m=3, y=3 x it is already given. at m= 1 3 , 3 y=x