Question

Equation of the curve passing through the point $(1,2)$ such that the intercept on the x-axis cut off between the tangent and origin is twice the abscissa is given by?

• A. $xy=2$
• B. $xy=1$
• C. $xy=2y$
• D. $y=-2x$

Answer 1

The correct option is D $y=-2x$

Slope of tangent $=\frac{dy}{dx}=\frac{y}{x-2x}=\frac{-y}{x}$

$\int \frac{dy}{y}=\int -\frac{dx}{x}\Rightarrow \ln y=-\ln x+C\Rightarrow \ln y=-\ln x+\ln C^{\prime }\Rightarrow y=-C^{\prime }x$

Given, $(1,2)$ lies on this curve $\Rightarrow$ $y=-2x$