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Find the eqution of the curve passing th...

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

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To find the equation of the curve passing through the point (1, 1) where the tangent at any point \( P(x, y) \) meets the coordinate axes at points \( A \) and \( B \) such that \( P \) is the midpoint of \( AB \), we can follow these steps: ### Step 1: Understand the Geometry Let \( P(x, y) \) be a point on the curve. The tangent at this point intersects the x-axis at point \( A \) and the y-axis at point \( B \). Since \( P \) is the midpoint of \( AB \), we can denote the coordinates of \( A \) and \( B \). ### Step 2: Determine Coordinates of Points A and B Assume the coordinates of point \( A \) are \( (2x, 0) \) and the coordinates of point \( B \) are \( (0, 2y) \). This is because the midpoint \( P \) is given by: \[ ...
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