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:
- A \(\frac{1}{2}\)
- B \(\pm \frac{1}{\sqrt{2}}\)
- C \(\pm 1\)
- D \(\pm \frac{1}{2 \sqrt{2}}\)
Answer & Solution
Correct Answer
(D) \(\pm \frac{1}{2 \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
\(m_1 = \frac{d}{dx}(y^2) = \frac{1}{2y}\) \(m_2 = \frac{d}{dx}(\frac{k}{x}) = -\frac{y}{x}\) \(m_1 m_2 = -1 \Rightarrow \left(\frac{1}{2y}\right)\left(-\frac{y}{x}\right) = -1\) \(-\frac{1}{2x} = -1 \Rightarrow x = \frac{1}{2}\)…
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