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Question
The family of curves in which the sub tangent at any point of a curve is double the abscissae, is given by
Options
x = Cy2
y = Cx2
x2 = Cy2
y = Cx
Solution
x = Cy2
\[\text{ Subtangent }= \frac{y}{\frac{dy}{dx}}\]
It is given that subtangent at any point of a curve is double of the abscissa.
\[\begin{array}{l}\therefore \frac{y}{\frac{dy}{dx}} = 2x \\ y = 2x\frac{dy}{dx} \\ \int\frac{dx}{x} = 2\int\frac{dy}{y} \\ \ln x = 2\ln y + a \\ \ln x = \ln y^2 + \ln c \\ \ln x = \ln c y^2 \\ x = c y^2\end{array}\]
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