Sect 10.2#3 equation of the tangent line to a parametric curve | Summary and Q&A

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April 22, 2016
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Sect 10.2#3 equation of the tangent line to a parametric curve

TL;DR

Learn how to find the equation of the tangent line to a parametric equation at a specific point by finding the slope and a point on the line.

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Questions & Answers

Q: How do we find the slope of the tangent line to a parametric equation?

To find the slope, we need to calculate the derivative of the y equation and divide it by the derivative of the x equation.

Q: How do we find a point on the tangent line to a parametric equation?

By plugging in a specific value of t into the parametric equations, we can find the corresponding x and y values, which give us a point on the line.

Q: What is the formula for the equation of a tangent line to a parametric equation?

The equation is given by y - y1 = m(x - x1), where m is the slope of the tangent line and (x1, y1) is a point on the line.

Q: How do we find the equation of the tangent line using the slope and a point?

By substituting the slope and the coordinates of the point into the formula y - y1 = m(x - x1), we can obtain the equation of the tangent line.

Summary & Key Takeaways

  • To find the equation of a tangent line to a parametric equation, we need to find the derivative, which gives us the slope of the tangent line.

  • The derivative is found by taking the derivative of the y equation and dividing it by the derivative of the x equation.

  • We also need a point on the tangent line, which can be found by plugging in a specific value of t into the parametric equations.

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