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Lecture

# 10.2 Calculus with Parametric Curves Question #2 (Medium)

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University of Toronto St. George

Mathematics

MAT136H1

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Winter

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10.2 Parametric Equations & Polar Coordinates
Calculus With Parametric Curves
Question #2 (Medium): Finding the Equation of the Tangent
Strategy
Any equation of a tangent line follows after linear slope intercept equation form:
So the goal is to find the slope and at the given parameter value , plug into each of
the parametric equations for coordinate. Then rearrange the equation to find the last value
which is the -intercept. Then by the definition of equation, leavand but only fill in theand .
Sample Question
Find the equation of the tangent to the curve at the point that corresponds to the given parameter value.
, ,
Solution
Any equation of tangent is given by a linear equation:

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