On comparing to the standard equation of circle with
x2+y2 + 2gx + 2fy +
C1 = 0
we get , g = - a , f = 0 ,
C1 =
c2 Here, centre
C1 = (-g , -f) = (a , 0)
and radius
(r1) =
√g2+f2−C1 =
√a2−c2 Equation of another circle is
x2+y2 - 2by +
x2 = 0 ... (ii)
Here, centre
C2 = (0 , b)
and radius
(r2) =
√b2−c2 As we know that, two circles touch each other externally, if
C1C2 =
r1+r2 ⇒
√a2+b2 =
√a2−c2+√b2−c2 Squaring both sides, we get
⇒
a2+b2 =
a2−c2+b2−c2 + 2
√a2−b2 √b2−c2 ⇒
2x2 = 2
√a2−b2 √b2−c2 ⇒
c2 =
√a2−b2 √b2−c2 Again squaring both sides, we get
⇒
x4 =
(a2−c2)(b2−c2) ⇒
c4 =
a2b2−a2c2−b2c2+c4 ⇒
a2c2+b2c2 =
a2b2 ... (ii)
Divide Eq. (iii) by
a2b2c2 , we get
⇒
+ =
⇒
=
+