Question

x+y=2 and x-y=2 are tangents of the circle. This circle touches another  circle which is expressed by x² + y² = 1

Find out the equation of the circle.

Answer 1

l₁ ​ =0,l₂ ​ =0 are tangent to required circle which intersect at A(2,0). The centre of the required circle will lie on bisector of acute angle between these tangents i.e. on

Let it be (h,0) where h is +ive and if r be the radius then it touches x² +y² =1 externally C₁C₂ ​ =r₁ ​ +r₂ ​ or h=1+r.....(1)

Hence the circles are (4− √2 ​,0).(√2 ​−1) and (√2 ,0),(√2 ​−1).