Find the equation of hyperbola having foci S(2, 1) and S'(10, 1) and a straight line `x+y-9=0` as its tangent.

Explanation

To find the equation of the hyperbola with given foci and a tangent line, we can follow these steps:

### Step 1: Identify the foci and find the center
The foci of the hyperbola are given as S(2, 1) and S'(10, 1). The center of the hyperbola is the midpoint of the line segment joining the foci.

\[ \text{Center} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = \left( \frac{2 + 10}{2}, \frac{1 + 1}{2} \right) = (6, 1) \]
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