The least distance between two points P and Q on the circle `x^(2) + y^(2) -8x + 10y + 37 =0` and `x^(2) + y^(2) + 16x + 55 = 0` is _______ .

Explanation

To find the least distance between two points P and Q on the circles defined by the equations \(x^2 + y^2 - 8x + 10y + 37 = 0\) and \(x^2 + y^2 + 16x + 55 = 0\), we will follow these steps:

### Step 1: Rewrite the equations of the circles in standard form

The general form of a circle is given by \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

**Circle 1:**
Given equation:
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