#### 4.1 2d tangents (27.5.02)

Does anyone outside there know of a package helping to plot the tangent to a 2d curve (not
being a circle) at a given point?

In Maple 8 you could compute the tangent line using the procedure TangentLine in the new
VectorCalculus package.

Otherwise, just compute it yourself: if it’s a parametric curve `x = X(t), y = Y(t)`

, the
tangent line at `t=t0`

is parametrically

x = X(t0) + D(X)(t0)*s, y = Y(t0) + D(Y)(t0)*s

Or if the curve is given implicitly by `F(x,y) = c`

and `[x0,y0]`

is a point on the curve where
the gradient of F is nonzero, the tangent line is given implicitly by

(x-x0)*D[1](F)(x0,y0) + (y-y0)*D[2](F)(x0,y0) = 0

or parametrically by

x = x0 + s*D[2](F)(x0,y0), y = y0 - s*D[2](F)(x0,y0)