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CUET · MATHS · PYQ PAPER 2023

If the curves \(x=y^2\) and \(x y=k\) meet at right angles, then the value of \(k\) is:

  1. A \(\frac{1}{2}\)
  2. B \(\pm \frac{1}{\sqrt{2}}\)
  3. C \(\pm 1\)
  4. D \(\pm \frac{1}{2 \sqrt{2}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\pm \frac{1}{2 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(m_1 = \frac{d}{dx}(y^2) = \frac{1}{2y}\) \(m_2 = \frac{d}{dx}(\frac{k}{x}) = -\frac{y}{x}\) \(m_1 m_2 = -1 \Rightarrow \left(\frac{1}{2y}\right)\left(-\frac{y}{x}\right) = -1\) \(-\frac{1}{2x} = -1 \Rightarrow x = \frac{1}{2}\)…