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A particle moves along the curve x^(2)=2...

A particle moves along the curve `x^(2)=2y`. At what point, ordinate increases at the same rate as abscissa increases ?

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To solve the problem, we need to find the point on the curve \( x^2 = 2y \) where the ordinate (y-coordinate) increases at the same rate as the abscissa (x-coordinate). This means we need to find when \( \frac{dx}{dt} = \frac{dy}{dt} \). ### Step-by-step solution: 1. **Differentiate the curve equation**: We start with the equation of the curve: \[ x^2 = 2y ...
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