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if x^(2)/a^(2) -y^(2)/b^(2) =1, " prove ...

if` x^(2)/a^(2) -y^(2)/b^(2) =1, " prove that " (d^(2)y)/(dx^(2)) = - b^(4)/(a^(2)y^(3))`

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To prove that \(\frac{d^2y}{dx^2} = -\frac{b^4}{a^2y^3}\) given the equation \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\), we will follow these steps: ### Step 1: Differentiate the given equation We start with the equation: \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \] Differentiating both sides with respect to \(x\): ...
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