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TS EAMCET · Maths · Application of Derivatives

If the curves \(x^2+p y^2=1\) and \(q x^2+y^2=1\) are orthogonal to each other, then

  1. A \(p-q=2\)
  2. B \(\frac{1}{p}-\frac{1}{q}=2\)
  3. C \(\frac{1}{p}+\frac{1}{q}=-2\)
  4. D \(\frac{1}{p}+\frac{1}{q}=2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{1}{p}+\frac{1}{q}=2\)

Step-by-step Solution

Detailed explanation

Given curves are \[ \begin{aligned} & x^2+p y^2=1 \\ & q x^2+y^2=1 \end{aligned} \] and On differentiating Eq. (i), w.r.t., \(x\) we get \[ \begin{gathered} 2 x+2 y p \frac{d y}{d x}=0 \\ \Rightarrow \quad \frac{d y}{d x}=m_1=-\frac{x}{p y} \end{gathered} \] On differentiating…