Intro to Plane Curves & Parametric Equations Examples | Calculus 2 - JK Math

Example Problems For How to Sketch Plane Curves & Eliminate the Parameter (Calculus 2) In this video we look at practice problems of sketching plane curves with parametric equations. We use the method of eliminating the parameter to find the corresponding rectangular equation to aid in sketching the curve, and find the initial point and terminal point of the curve when applicable to complete the sketch with a direction. We also look at examples of finding sets of parametric equations for a given rectangular equation or for a set of specific requirements/characteristics of a plane curve. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 Example 1 - Sketch Plane Curve: x=t/3+3, y=2t-4, [0,3] 8:03 Example 2 - Sketch Plane Curve: x=t-5, y=sqrt(t) 14:18 Example 3 - Sketch Plane Curve: x=4cosθ, y=3sinθ, [0,2π] 24:45 Example 4 - Eliminate Parameter: x=e^(-t), y=e^(2t)-1 28:19 Example 5 - Eliminate Parameter: x=sin(t), y=cos(2t) 29:36 Example 6 - Eliminate Parameter: x=secθ, y=tan^2(θ) 30:55 Example 7 - Find Parametric Equations: Circle, centered at (3,1), r=2 35:24 Example 8 - Find Parametric Equations: y=x^2, t=4 at (4,16) 36:38 Example 9 - Find Parametric Equations: y=4x+1, t=-1 at (-2,-7) 37:44 Example 10 - Find Parametric Equations: y=8x-1 39:05 Example 11 - Find Parametric Equations: y=4/(x-1) 40:04 Outro 📝 Lesson Video For These Examples:    • Intro to Plane Curves & Parametric Equatio...   ⏩ Next Lesson:    • Parametric Derivatives | Calculus 2 Lesson...   📺 Calculus 2 Playlist:    • Calculus 2   📺 Calculus 1 Playlist:    • Calculus 1   🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook:   / jkmathematics   Twitter:   / jk_mathematics   Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.