In this video I go over another example on conic sections in polar coordinates and this time sketch a hyperbola in polar coordinates. The hyperbola is given by the formula r = 12/(2 + 4sinθ) which can be rewritten to r = 6/(1 + 2sinθ) to be in the standard conic form, r = e∙d(1 + e∙sinθ). Thus with an eccentricity e = 2, a directrix y = d = 3, and determining the vertices and x-intercepts we can graph the hyperbola. Also for more accuracy I show that the asymptote lines are parallel to the angles θ = 7π/6 and θ = - π/6. Later in the video I briefly mentioned about determining the exact polar equations of the asymptote lines, which will be a topic of further research so stay tuned! This is a great and extensive example on determining the properties of a conic in polar coordinates and manually sketching it in a step-by-step methodology; so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5sK1cp-4X1eVV1s7w
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/conics-in-polar-coordinates-example-4-hyperbola
Related Videos:
Conics in Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H4OJpJ2gslXVLT8mP-SgJP
Conic Sections Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FEUsuxP3KS5DRbidSSGBPL
Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUFiPLsYw5_Ljd5riOUzjP
Conics in Polar Coordinates: Example 2: Ellipse:
Exact Trigonometry Ratios Part 1: 0, 30, 45, 60, and 90 Degrees: .
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
Official Website: https://MES.fm
Steemit: https://steemit.com/@mes
Gab: https://gab.ai/matheasysolutions
Minds: https://minds.com/matheasysolutions
Twitter: https://twitter.com/MathEasySolns
Facebook: https://fb.com/MathEasySolutions
Google Plus: https://mes.fm/gplus
LinkedIn: https://mes.fm/linkedin
Pinterest: https://pinterest.com/MathEasySolns
Instagram: https://instagram.com/MathEasySolutions
Email me: [email protected]
Try our Free Calculators: https://mes.fm/calculators
BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm
Try our Free Online Tools: https://mes.fm/tools
iPhone and Android Apps: https://mes.fm/mobile-apps
▶️ DTube
▶️ IPFS
I don't always sketch a hyperbola in polar coordinates but when I do I usually determine the asymptote lines indirectly as being parallel to a couple of polar angles ;)
View Video Notes: https://steemit.com/mathematics/@mes/conics-in-polar-coordinates-example-4-hyperbola