Question

Find the equation of common chord of the two circles is (x-a)^2+(y-b)^2=c^2,(x-b)^2+(y-a)^2=c^2​

Answer 1

Step-by-step explanation:

S

1

=(x−a)

2

+(y−b)

2

=c

2

&r

1

=c:c

1

=(a,b)

S

2

=(x−b)

2

+(y−a)

2

=c

2

&r

2

=c:c

2

=(b,a)

Equ

n

ofcommonchord=s

1

−s

2

=0

⇒x

2

+a

2

−2ax+y

2

+b

2

−2by+c

2

−x

2

−b

2

+2bx−y

2

−a

2

+2ay−c

2

=0

⇒−2x(a−b)+2y(a−b)=0

⇒(a−b)(2y−2x)=0

∴x−y=0

d−perpendiculardistanceofc

1

(a,b)tox−y=0

=

2

∣(a−b)∣

Lengthofchord=2

r

1

2

−d

2

=2

c

2

−

2

(a−b)

2

=

2(2c

2

−(a−b)

2

)

=

4c

2

−2(a−b)

2