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TS EAMCET · Maths · Differentiation

If \(x^2+y^2=t-\frac{1}{t}, x^4+y^4=t^2+\frac{1}{t^2}\) then \(\frac{d y}{d x}=\)

  1. A \(\frac{x}{y}\)
  2. B \(\frac{-x}{y}\)
  3. C \(\frac{y}{x}\)
  4. D \(\frac{-y}{x}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{-y}{x}\)

Step-by-step Solution

Detailed explanation

Given \(\mathrm{x}^2+\mathrm{y}^2=\mathrm{t}-\frac{1}{\mathrm{t}}\) \(\begin{aligned} & \text { and } x^4+y^4=t^2+\frac{1}{t^2} \\ & \Rightarrow x^4+y^4=x^4+y^4+2 x^2 y^2+2 \\ & \Rightarrow x^2 y^2+1=0 \end{aligned}\) Now \(\frac{d y}{d x} \Rightarrow 2 x y^2+x^2 2 y y l=0\)…