Question

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

Answer 1

this is Ur required result

Answer 2

Equation of the other tangent is y = x/3.

y = 3x is a tangent to the circle with centre(1,1). The distance between the tangent and the centre of the circle is equal to the radius of the circle.

Using distance formula ,

d = r = |1-3|/√10

r = 2/√10

Equation of the circle , (x-1)² + (y-1)² = 4/10

Another tangent is drawn to the circle from the origin.

Equation of the tangent , y -0 = m(x-0)

=> y = mx

Using distance formula ,

=> r = |1-m|/√(1+m²)

=> 2/√10 = |1-m| / √(1+m²)

=> 4/10 = (1-m)² / (1+m²)

=> (3m-1) (m-3) = 0

m = 1/3 , 3

The equation of the other tangent , y = x/3.