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The tangent line of a function at a point is the line which is tangent to the function at the point, meaning that it only intersects the line at a single point there. The slope of the tangent line at a point is the slope of the function at that point.

The tangent line to a single variable function was the line in two-dimensional space that represented the slope of the single variable function. Similarly, the tangent plane to a multivariable function is the plane in three-dimensional space that represents the slope of the multivariable function. To find the equation of the tangent plane, you need The slope of the function at the point of tangency in the direction of each independent variable (the...

This video tutorial works through math problems/equations that address topics in Calculus 2, Polar & Parametric. This specific tutorial addresses Tangent lines.

This video tutorial works through math problems/equations that address topics in Calculus 3, Partial Derivatives. This specific tutorial addresses Equation of the tangent plane.

This video tutorial works through math problems/equations that address topics in Calculus 3, Vectors. This specific tutorial addresses Parametric equations of the tangent line.

This video tutorial works through math problems/equations that address topics in Calculus 3, Vectors. This specific tutorial addresses Tangent plane to the parametric surface.

You'll find the equation of the tangent line to a parametric equation in the same way that you found the tangent line to a regular equation. The only thing that's different is how you take the derivative of a parametric curve versus a regular curve, and that you have to plug a t-value into both x(t) and y(t) to find the coordinate point that represents the point of tangency.