JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the curves \(x=y^{4}\) and \(x y=k\) cut at right angles, then \((4 k )^{6}\) is equal to ..... .
- A \(5\)
- B \(3\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(x=y^{4} x y=k\) for intersection \(\quad y ^{5}= k \ldots(1)\) Also \(x=y^{4}\) \(\Rightarrow 1=4 y ^{3} \frac{ dy }{ dx } \Rightarrow \frac{ dy }{ dx }=\frac{1}{4 y ^{3}}\) for \(x y=k \Rightarrow x=\frac{k}{y}\) \(\Rightarrow 1=-\frac{ k }{ y ^{2}} \cdot \frac{ dy }{ dx }\)…
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