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, we need to find the equation of the curve given that at any point \((x, y)\) on the curve, the slope of the tangent is twice the slope of the line segment joining the point \((-4, -3)\) to \((x, y)\). The curve passes through the point \((-2, 1)\).

### Step-by-Step Solution:

1. **Determine the Slope of the Line Segment:**
The slope of the line segment joining the points \((x, y)\) and \((-4, -3)\) can be calculated using the formula:
\[
\text{slope} = \frac{y - (-3)}{x - (-4)} = \frac{y + 3}{x + 4}
...