Question

If the circles x2+y2+2cx+b=0 and x2+y2+cx+b=0 touch each other, then

Answer 1

Answer:

If the circles x2+y2+2cx+b=0 and x2+y2+cx+b=0 touch each other, then

Step-by-step explanation:

(a+b) 2 =2c

S 1 :x 2 +y 2 +2ax+2by+c=0⇒ represents the circle with centre C 1 ≡(−a,−b) & radius r 1 = a 2 +b 2 −c

S 2 :x 2 +y 2 +2bx+2ay+c=0⇒ represents the circle with centre C 2 ≡(−b,−a) & radius r 2 = a2+b 2 −c

Distance between centre = (a−b) 2 +(a−b) 2 = 2

(a−b)

case - 12 (a−b)=r 1 +r 2 =2 a 2 +b 2 −c

( touching externally )2a 2 +2b 2 −4ab=4a 2 +4b2 −4c2a 2 +2b 2 +4ab=4c(a+b) 2 =2c

case - 22

(a−b)=r 1 −r 2

=0 ( Touching internally ) which is not possible.