Find the condition for the curves frac{x^2}{a | vedclass

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(B) Given curves are $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(1)$ and $xy = c^2$ $(2)$.Differentiating $(1)$ with respect to $x$: $\frac{2x}{a^2} - \

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$a^2 = b^2$

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(B) Given curves are $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ $(1)$ and $xy = c^2$ $(2)$.Differentiating $(1)$ with respect to $x$: $\frac{2x}{a^2} - \frac{2y}{b^2} \frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = \frac{b^2x}{a^2y}$. Let this be $m_1$.Differentiating $(2)$ with respect to $x$: $y + x \frac{dy}{dx} = 0 \Rightarrow \frac{dy}{dx} = -\frac{y}{x}$. Let this be $m_2$.For the curves to intersect orthogonally,$m_1 	imes m_2 = -1$.$\left( \frac{b^2x}{a^2y} ight) \left( -\frac{y}{x} ight) = -1$.$-\frac{b^2}{a^2} = -1 \Rightarrow a^2 = b^2$.

Find the condition for the curves $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and $xy = c^2$ to intersect orthogonally.

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