Finding Equations of Tangent Lines In Exercises 27-30, find the equations of the tangent lines at the point where the curve crosses itself.
To calculate: The Equation of the tangent line at the point where curve crosses itself of the equation, and .
The parametric equation, and .
If a smooth curve C given by the equation and . Then the slope of the curve C is, .
Consider the provided parametric function,
Procedure to draw the graph of the parametric equation through Ti-83,
Step1: Press ON key.
Step2: Press MODE key. Then select “Par” and press Enter key.
Step3: Press key.
Step4: Enter the parametric equation “ and .
Step4: Set window key and .
Step5: Press TRACE key.
The graph of the parametric function is,
From the above figure, the curve crosses itself at the point . Now calculate the value of parameter at that point.
Consider the equation,
Substitute in the above equation and find the value of t,
Again, consider the parametric function,
Differentiate the above equation with respect to ,
Now, consider the parametric function,
Differentiate the above function with respect to ,
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