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