Find the equation of the hyperbola whose directrix is `2x+y=1,` focu`s(1,2)` and eccentricity `sqrt(3)dot`

Explanation

To find the equation of the hyperbola with the given directrix, focus, and eccentricity, we can follow these steps:

### Step 1: Understand the relationship
The relationship for a hyperbola is given by the equation:
\[ PS = E \cdot PM \]
Where:
- \( PS \) is the distance from any point \( P(x, y) \) on the hyperbola to the focus \( S(1, 2) \).
- \( PM \) is the perpendicular distance from the point \( P(x, y) \) to the directrix \( 2x + y - 1 = 0 \).
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