Question

If $x^{2}+y^{2}=t+\frac{1}{t}$ and $x^{4}+y^{4}=t^{2}+\frac{1}{t^{2}}$, then $\frac{dy}{dx}$ is equal to

• A. $\frac{y}{x}$
• B. $\frac{-y}{x}$
• C. $\frac{x}{y}$
• D. $\frac{-x}{y}$

Hint:

Logic Tip: Alternatively, from $x^2y^2 = 1$, we get $xy = 1$ (for 1st quadrant). Differentiating gives $x\frac{dy}{dx} + y = 0 \implies \frac{dy}{dx} = -\frac{y}{x}$. Taking the root before differentiating simplifies the product rule application!

Answer 1

The Correct Option is B