Ernstfalld

2021-02-06

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

Bertha Stark

Step 1 To determine the parametric equations for a line passing through a given point, create the expression.

Step 2 The parametric equations for the curves should be written as follows.

Step 3 Write the vector equation from the parametric equations of the curve as follows.

Step 4 The derivative of the vector function r is the tangent vector of the curve (t). To find the derivative of the vector function, differentiate each component of the vector function.

Step 5 Given that the point . That is,

As the specified point , consider the value of scalar parameter t as 0 and substitute in the parametric equations of the curve to obtain the point, which is on the required line. Substitute 0 for t in equation (2),

The point on the required line is  As the point on the required line is same as the specified point  Step 6 Substitute 0 for t in <

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