# Find the tangent line(s) to the parametric curve given by x=t^5-4t^3 y=t^2

Find the tangent line(s) to the parametric curve given by
$x={t}^{5}-4{t}^{3}$
$y={t}^{2}$
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Alannej
$x={t}^{5}-4{t}^{3}$
$y={t}^{2}$
$m=\frac{dy}{dx}=\frac{2t}{5{t}^{4}-12{t}^{2}}$
$⇒\frac{2}{5{t}^{3}-12t}\left[\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}\right]$
line of tangent
$Y-{y}_{1}=m\left(x-{x}_{1}\right)$
$Y-{t}^{2}=\frac{2}{5}{t}^{3}-12t\left(x-{t}^{5}+4{t}^{3}\right)$