CUET · MATHS · PYQ PAPER 2025
The curve \(x=y^2\) and \(x y=k\) cut orthogonally, then \(k^2\) is equal to :
- A 1
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{8}\)
Step-by-step Solution
Detailed explanation
\(x=y^2 \implies \frac{dy}{dx}_1 = \frac{1}{2y}\) \(xy=k \implies y + x\frac{dy}{dx}_2 = 0 \implies \frac{dy}{dx}_2 = -\frac{y}{x}\) \(\frac{dy}{dx}_1 \cdot \frac{dy}{dx}_2 = -1 \implies \left(\frac{1}{2y}\right) \left(-\frac{y}{x}\right) = -1\)…
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