Question

If the tangent at any point $(x,y)$ of a curve intercepts equal lengths on the coordinate axes, then the differential equation of the curve is:

• A. $\dfrac{dy}{dx}=\dfrac{y}{x}$
• B. $\dfrac{dy}{dx}=-\dfrac{y}{x}$
• C. $\dfrac{dy}{dx}=x+y$
• D. $\dfrac{dy}{dx}=x-y$

Hint:

Whenever a tangent cuts intercepts on axes, immediately think about intercept form: \[ \frac{x}{a}+\frac{y}{b}=1 \] and use the geometric condition relating $a$ and $b$.

Answer 1

The Correct Option is B