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At any point (x,y) of a curve, the slope...

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)

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To solve the problem, we need to find the equation of the curve given that at any point \( P(x, y) \) of the curve, the slope of the tangent is twice the slope of the line segment joining the point of contact to the point \((-4, -3)\). The curve also passes through the point \((-2, 1)\). ### Step-by-Step Solution: 1. **Identify the slope of the tangent**: The slope of the tangent at point \( P(x, y) \) is given by \( \frac{dy}{dx} \). 2. **Calculate the slope of the line segment**: ...
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