Question

The number of common tangents of the circles (x + 3)2 + (y-2)2 = 49 and
(x - 2)2 + (y + 1)2 = 4 is​

Answer 1

Answer:

Let S

1

:x

2

+y

2

−2x−1=0 and S

2

:x

2

+y

2

−2y−7=0

⇒C

1

=(1,0),r

1

=

1+1

=

2

,C

2

=(0,1),r

2

=

1+7

=2

2

Now C

1

C

2

=

1+1

=

2

. Clearly C

1

C

2

=r

2

−r

1

Therefore circle S

1

touches S

2

internally.Thus there will exist only one common tangent.