Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric equations x = t2 − t, y = (2t3 − 11)2/3 - Look for the value of t which corresponds to the point A on D. - Obtain the equation (in point-slope form) of the tangent line to D at the point A.

Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric equations x = t2 − t, y = (2t3 − 11)2/3 - Look for the value of t which corresponds to the point A on D. - Obtain the equation (in point-slope form) of the tangent line to D at the point A.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 45CT

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Question

Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric equations

x = t² − t,

y = (2t³ − 11)^2/3

- Look for the value of t which corresponds to the point A on D.

- Obtain the equation (in point-slope form) of the tangent line to D at the point A.

Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)

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