Find the length of the chord of contact with respect to the point on the director circle of circle `x^2+y^2+2a x-2b y+a^2-b^2=0` .

Explanation

To find the length of the chord of contact with respect to the point on the director circle of the given circle \( x^2 + y^2 + 2ax - 2by + a^2 - b^2 = 0 \), we will follow these steps:

### Step 1: Identify the center and radius of the given circle
The given circle can be rewritten in standard form. The center \((h, k)\) of the circle is given by:
\[ h = -\frac{2a}{2} = -a, \quad k = \frac{2b}{2} = b \]
Thus, the center of the circle is \((-a, b)\).
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