Question

The line y = x is tangent at (0,0) to a circle of radius 1. The centre of the circle is : ​

Answer 1

Answer:

equatio of cicle with radius =

′

1

′

(x−a)

2

+(y−b)

2

=1

(a,b)→center

given y=x is a target

slope of target =1

perpendicular distance from center to target radius target radius

⇒

1

2

+1

2

∣b−a∣

=1 equatio of target

⇒

2

∣b−a∣

=1 2(x−a)+2(y−b)y

′

=0

⇒

∣b−a∣=

2

⇒y

′

=

(Y−B)

(x−a)

Giveny

′

=1 At (x,y)=(0,0)

⇒1=−

b

a

⇒

b=−a

From (1) and (2)

(−a−a)=

2

a=

2

−1

a=

2

1

△b=

2

1

b=

2

−1

(a,b)=(

2

−1

,

2

1

)

∴(a,b)=(

2

1

,

2

−1

)