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strategy

strategy - the point A x A y A → substitute A into the...

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Problem Assume that the tangent lines to the curve (C): f ( x, y ) = 0 pass through the point A ( x A , y A ). Find the coordinates of the points where these tangent lines intersect the curve (C). Strategy Step 1 : Find dy dx or y 0 ( x ). Step 2 : Let the points where the tangent lines intersect the curve (C) be P ( x P , y P ), i.e., f ( x P , y P ) = 0 because P lies on the curve (C). the slope of the tangent lines at P ( x P , y P ) is m = dy dx computed at ( x P , y P ). Step 3 : Use the point-slope formula to write the equation of these tangent lines: y - y P = m ( x - x P ) Step 4 : These tangent lines pass through
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Unformatted text preview: the point A ( x A , y A ) → substitute A into the equation of the tangent lines in Step 3. Then use the information from Step 2 ( f ( x P , y P ) = 0) to solve for x P . • Step 5 : After solving for x P , then ﬁnd y P . Notice : If you are asked to write the equations of these tangent lines, just go back to Step 3 and substitute each point ( x P , y P ) into the equation of the tangent line. Practice Problems : Question 4 in the Review Set for Test 2 and Problem 16 in Section 3.5. 1...
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