Question:medium
If \( x = a \cos^3 \theta \) and \( y = a \sin^3 \theta \), then \( 1 + \left( \frac{dy}{dx} \right)^2 \) is:
If \( x = a \cos^3 \theta \) and \( y = a \sin^3 \theta \), then \( 1 + \left( \frac{dy}{dx} \right)^2 \) is:
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The parametric equations $x = a \cos^3 \theta, y = a \sin^3 \theta$ represent an Astroid. For such curves, the derivative often simplifies to a simple power or ratio of $\tan \theta$.
Updated On: May 6, 2026
- \( \tan \theta \)
- \( \tan^2 \theta \)
- \( 1 \)
- \( \sec^2 \theta \)
- \( \sec \theta \)
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The Correct Option is D
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