If the circles `x^2+y^2+2a x+c=0a n dx^2+y^2+2b y+c=0` touch each other, then `1/(a^2)+1/(b^2)=1/c` (b) `1/(a^2)+1/(b^2)=1/(c^2)` (c) `a+b=2c` (d) `1/a+1/b=2/c`

Explanation

To solve the problem, we need to analyze the given equations of the circles and derive the relationship between \( a \), \( b \), and \( c \) under the condition that the circles touch each other.

### Step-by-Step Solution:

1. **Identify the equations of the circles**:
The equations of the circles are given as:
\[
x^2 + y^2 + 2ax + c = 0 \quad \text{(Circle 1)}
...