Find the equation of circle passing through the origin and cutting the circles
`x^(2) + y^(2) -4x + 6y + 10 =0` and `x^(2) + y^(2) + 12y + 6 =0` orthogonally.

Explanation

To find the equation of the circle that passes through the origin and cuts the given circles orthogonally, we can follow these steps:

### Step 1: Write the general equation of the circle
The general equation of a circle can be written as:
\[ x^2 + y^2 + 2gx + 2fy + c = 0 \]
Since the circle passes through the origin (0, 0), we can substitute \(x = 0\) and \(y = 0\):
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