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Question
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is ______.
Options
An ellipse
Parabola
Circle
Rectangular hyperbola
Solution
The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is rectangular hyperbola.
Explanation:
Since, the slope of the tangent to the curve = x : y
∴ `("d"y)/("d"x) = x/y`
⇒ ydy = xdx
Integrating both sides, we get
`int "y" "d"y = int x "d"x`
⇒ `y^2/2 = x^2/2 + "c"`
⇒ y2 = x2 + 2c
⇒ y2 – x2 = 2c = k which is rectangular hyperbola.
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