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

Answer 1

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.

\[\begin{array}{l}\therefore \frac{y}{\frac{dy}{dx}} = 2x \\ y = 2x\frac{dy}{dx} \\ \int\frac{dx}{x} = 2\int\frac{dy}{y} \\ \ln x = 2\ln y + a \\ \ln x = \ln y^2 + \ln c \\ \ln x = \ln c y^2 \\ x = c y^2\end{array}\]