Question

The equation of tangent line
at the given of the parameter
will be
x=vt, y = 2t at t = 4​

Answer 1

Answer:

find the equation of the tangent line, we need the slope 

m=dydx and the point of tangency (xo,yo).

Then the equation is the usual y−yo=m(x−xo).

We have the parametric curve x=t4+1,y=t3+t,

so we compute dxdt=4t3anddydt=3t2+1.

The chain rule dydt=dydx⋅dxdt says that dydx=dydtdxdt.

So we use the derivatives of the parametric equations:

dydx=3t2+14t3. Now put in t=−1 and find:

m=dydx=3⋅(−1)2+