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The curve for which the slope of the tan...

The curve for which the slope of the tangent at any point is equal to the ration of the abcissa to the ordinate of the point is

A

an ellipse

B

parabola

C

circle

D

rectangular hyperbola

Text Solution

AI Generated Solution

To solve the problem, we need to find the curve for which the slope of the tangent at any point is equal to the ratio of the abscissa (x-coordinate) to the ordinate (y-coordinate) of the point. Let's denote the curve as \( y = f(x) \). The slope of the tangent at any point on the curve can be represented as \( \frac{dy}{dx} \). According to the problem, this slope is equal to the ratio of the abscissa to the ordinate, which can be expressed mathematically as: \[ \frac{dy}{dx} = \frac{x}{y} \] ...
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