Hello,
[tex]
x=a*cos(t)==\ \textgreater \ \dfrac{dx}{dt} =-a*sin(t)\\
y=a*sin(t)==\ \textgreater \ \dfrac{dy}{dt}=a*cos(t)\\
\dfrac{dy}{dx} =- \dfrac{1}{tan(t)} \\\\
x= \dfrac{a}{2} ==\ \textgreater \ \\\\
cos(t)= \dfrac{1}{2} ==\ \textgreater \ t= \dfrac{\pi}{3} ==\ \textgreater \ y=a* \dfrac{\sqrt{3}}{2} \\\\
y'=- \dfrac{\sqrt{3}}{3} \\\\
\textrm{Equation of the tangent :}\\
y-a*\dfrac{\sqrt{3}}{2}=(x-\dfrac{a}{2} )*(- \dfrac{\sqrt{3}}{3})\\\\
y=- \dfrac{ \sqrt{3} }{3} *x+2*a*\dfrac{\sqrt{3}}{3}\\\\
\boxed{3y= \sqrt{3} *(2a-x)}
[/tex]
