If x = a sec^{2} theta and y = a tan^{2} thet | vedclass

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(D) Given $x = a \sec^{2} 	heta$ and $y = a 	an^{2} 	heta$.Differentiating $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a \cdot 2 \sec 	heta

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(D) Given $x = a \sec^{2} 	heta$ and $y = a 	an^{2} 	heta$.Differentiating $x$ with respect to $	heta$:$\frac{dx}{d	heta} = a \cdot 2 \sec 	heta \cdot (\sec 	heta 	an 	heta) = 2a \sec^{2} 	heta 	an 	heta$.Differentiating $y$ with respect to $	heta$:$\frac{dy}{d	heta} = a \cdot 2 	an 	heta \cdot (\sec^{2} 	heta) = 2a 	an 	heta \sec^{2} 	heta$.Now,find $\frac{dy}{dx}$ using the chain rule:$\frac{dy}{dx} = \frac{dy/d	heta}{dx/d	heta} = \frac{2a 	an 	heta \sec^{2} 	heta}{2a \sec^{2} 	heta 	an 	heta} = 1$.Finally,differentiate $\frac{dy}{dx}$ with respect to $x$ to find the second derivative:$\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(1) = 0$.

If $x = a \sec^{2} \theta$ and $y = a \tan^{2} \theta$,then find $\frac{d^{2} y}{d x^{2}}$.

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