grog said:so I would end up with 4x-2y and zero for the two normal vectors? and then take the cross product of the two? I think I may be confusing some concepts here.
Parametric equations of a tangent line are equations that describe the coordinates of a point on a curve at a specific position, usually in terms of a parameter, such as time or distance.
To find the parametric equations of a tangent line, you first need to find the derivative of the curve at the given point. Then, use this derivative to find the slope of the tangent line. Finally, use the point-slope form of a line to write the parametric equations.
Parametric equations of tangent lines are useful because they allow us to represent a curve in a more simplified way. They also help us to find the coordinates of points on the curve at specific positions, which is important in many applications, such as physics and engineering.
Yes, it is possible to find parametric equations of a tangent line for any curve as long as the curve is differentiable at the given point. If the curve is not differentiable, the tangent line does not exist.
Yes, it is possible to have more than one tangent line at a given point. This can happen if the curve has a sharp point or cusp at that point. In this case, each tangent line would have a different slope and therefore different parametric equations.