#### 2d tangents (27.5.02)

##### Dr. U. Kasper (23.10.01)

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?

##### Robert Israel (30.5.02)

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)