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.

Transcript

I will show you how we are going to find an equation of the line tangent to this parametric equation at t is equal to 1 so remember we have to have two things whenever one to find the equation of the tangent line first we need to get interrogative and the derivative in this case is that we need to get dy/dx this will tell you the slope of the tange... Read More

Key Insights

• 🫥 The equation of a tangent line to a parametric equation requires finding the slope and a point on the line.
• ❣️ The derivative of the y equation divided by the derivative of the x equation gives us the slope of the tangent line.
• 🫥 Plugging a specific value of t into the parametric equations helps us find a point on the tangent 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.