Continuity and Differentiability
NCERT Class 12
CBSE
Grade 12
Question:
Find $\dfrac{dy}{dx}$ if $x = a \cos^2 \theta, y = b \sin^2 \theta$.
Step-by-Step Solution
$\dfrac{dx}{d\theta} = -a \sin 2\theta, \dfrac{dy}{d\theta} = b \sin 2\theta$. [1.0 Mark]
$\dfrac{dy}{dx} = \dfrac{b \sin 2\theta}{-a \sin 2\theta} = -\dfrac{b}{a}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating parametric components: 1.0 Mark
Evaluating derivative $= -b/a$: 1.0 Mark
Correct Answer:
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