Question

Centre of the circle meeting each of the three circles
x2 + y2 = 1, x2 + y2 – X+2y = 4
& x² + y2 - 2x+y+2 = 0
orthogonally, is

Answer 1

Answer:

The given circles are

S

1

:x

2

+y

2

+2gx+2fy+c=0 ...(1)

and, S

2

:x

2

+y

2

+2g

′

x+2f

′

y+c

′

=0 ...(2)

The equation of common chord of (1) and (2) is

S

1

−S

2

=0

i.e., 2(g−g

′

)x+2(f−f

′

)y+(c−c

′

)=0 ...(3)

Since (1) bisects the circumference of (2), therefore common chord will be the diameter of circle (2)

∴ Center (−g

′

,−f

′

) of circle (2) lies on (3).

∴−2(g−g

′

)g

′

−2(f−f

′

)f

′

+c−c

′

=0

or, 2g

′

(g−g

′

)+2f

′

(f−f

′

)=c−c

′

.