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# Solution for Find the Slope of the Tangent and the Normal to the Following Curve at the Indicted Point X = a Cos3 θ, Y = a Sin3 θ at θ = π/4 ? - CBSE (Science) Class 12 - Mathematics

#### Question

Find the slope of the tangent and the normal to the following curve at the indicted point  x = a cos3 θ, y = a sin3 θ at θ = π/4 ?

#### Solution

$x = a \cos^3 \theta$

$\Rightarrow \frac{dx}{d\theta} = - 3a \cos^2 \theta \sin \theta$

$y = a \sin^3 \theta$

$\Rightarrow \frac{dy}{d\theta} = 3a \sin^2 \theta \cos \theta$

$\therefore \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = \frac{3a \sin^2 \theta \cos \theta}{- 3a \cos^2 \theta \sin \theta} = - \tan \theta$

$\text { Now, }$

$\text { Slope of the tangent }= \left( \frac{dy}{dx} \right)_\theta = \frac{\pi}{4} =-tan\frac{\pi}{4}=-1$

$\text { Slope of the normal }=\frac{- 1}{\left( \frac{dy}{dx} \right)_\theta = \frac{\pi}{4}}=\frac{- 1}{- 1}=1$

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Solution for question: Find the Slope of the Tangent and the Normal to the Following Curve at the Indicted Point X = a Cos3 θ, Y = a Sin3 θ at θ = π/4 ? concept: Tangents and Normals. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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