Implicit Differentiation

This animation visualizes the implicit differentiation of the hyperbola $x^2 - y^2 = 4xy + 2$, showing how a sliding secant line converges to the tangent at a specific point $P$ where the slope is exactly $1/2$. It then steps through the algebraic derivation line-by-line, concluding at the curve's vertex where the denominator vanishes and the tangent line becomes vertical.