Question

The equation of a circle which touches the line x – y + 1 = 0 at the point (0,1) and passing through the point (1,1) is

Answer 1

ANSWER

The line x - y = 0 touches at (0,0)

S

1

⇒x

2

+y

2

+λ(x−y)=0 .......(1)

S

2

⇒x

2

+y

2

+2y−3=0 .............(2)

S

1

bisects the circumference of S

2

.

Common chord S

1

−S

2

=0 passes through the centre (0,-1) of S

2

.

∴λ(x−y)−2y+3=0

λ+2+3=0⇒λ=−5 ∴ put in (1)

x

2

+y

2

−5x+5y=0