Question

Find the equation of the circle which cuts orthogonally the 3 circles

Answer 1

Answer:

0

Step-by-step explanation:

Let the circle be x

2

+y

2

+2gx+2fy+d=0

For two circles to be orthogonal, 2gg

′

+2ff

′

=c+c

′

So from the question,

d−a

2

=0.......(1)

2.g.(−c)=d+c

2

−a

2

........(2)

2.f.(−b)=d+b

2

−a

2

..........(3)

Solving (1),(2) and (3), we get

g=−

2

c

f=−

2

b

d=a

2

So the circle is,

x

2

+y

2

−cx−by+a

2

=0