Question

Please help me differentiate this

A curve is defined by the parametric equations
x=t^2 and y=t^3
show that the equation of the tangent to the curve at the point P (p^2, p^3) is
2y-3px+p^3=0

Answer 1

Hello,


`x=t^2===\ \textgreater \ dx=2tdt\\\\ y=t^3===\ \textgreater \ dy=3t^2dt\\\\ (dy)/(dx) = (3)/(2) t\\\\ P=(p^2;p^3)===\ \textgreater \ t=p\\\\ Equation\ of\ the\ tangent:\\ y-p^3= (3)/(2)p(x-p^2)\\ ===\ \textgreater \ 2y-3px+p^3=0\\\\`