I can only suggest the format is not as required. It says to type an equation, but 5x+21 is not such.archaic said:
haruspex said:
A parametrized curve is a curve that is defined by a set of equations, known as parametric equations, that describe the coordinates of points on the curve in terms of one or more parameters.
A tangent to a parametrized curve is a straight line that touches the curve at a specific point and has the same slope as the curve at that point. It represents the instantaneous direction of the curve at that point.
To find the tangent to a parametrized curve, you can use the derivative of the parametric equations. The derivative represents the slope of the curve at any given point, so by finding the derivative and plugging in the coordinates of the point, you can determine the slope of the tangent line.
The tangent to a parametrized curve is important because it helps us understand the behavior of the curve at a specific point. It can also be used to find the rate of change or velocity of an object following the curve.
Yes, a parametrized curve can have multiple tangents at the same point if the curve has a sharp turn or point of inflection at that point. In this case, the curve may have both a left and right tangent at that point.