Question

The equations of two circles in the xy-
plane are given by
(x – 7)^2+(y + 1)^2 = 64, and (x – 5)^2 + (y + 2)^2= 4
At how many points do the two circles
intersect?

Answer 1

Answer:

Circle S1 is x

2

+y

2

=16

Circle S2 is x

2

+y

2

−2y=0

Centre C1 is C

1

(0,0) and radius R

1

=4

Centre C2 is C

2

(0,1) and radius R

2

=1

Distance between Centres is C

1

C

2

=1

Since C

1

C

2

<∣R

2

−R

1

∣

Circle S2 is completely inside S1

⟹ No common tangents