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COMEDK · Maths · 27. Application of Derivatives

The length of the subtangent to the curve \(x^{2} y^{2}=a^{4}\) at \((-a, a)\) is

  1. A \(2 a\)
  2. B \(a / 2 \quad\)
  3. C \(a / 3\)
  4. D \(a\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(a\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} &x^{2} y^{2}=a^{4} \Rightarrow 2 x y^{2}+x^{2}\left(2 y y^{\prime}\right)=0 \\ &\Rightarrow \quad y^{r}=\frac{-2 x y^{2}}{2 x^{2} y}=\frac{-y}{x} \\ &\left.\therefore \quad \frac{d y}{d x}\right|_{(-a, a)}=\frac{-a}{-a}=1 \end{aligned} \] Now, length…