At any point (x, y) of a curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point `(" "4," "3)` . Find the equation of the curve given that it passes through `(2," "1)` .

Explanation

To solve the problem step by step, we will derive the equation of the curve based on the given conditions.

### Step 1: Understanding the Problem
We need to find the equation of a curve where the slope of the tangent at any point \((x, y)\) is twice the slope of the line segment joining that point to the point \((4, 3)\).

### Step 2: Expressing the Slopes
Let the slope of the tangent at point \((x, y)\) be represented by \(\frac{dy}{dx}\). The slope of the line segment joining \((x, y)\) to \((4, 3)\) can be expressed as:
\[
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