Shifted Conics: Ellipses (and Circles)
In this video I go over further into conics and this time look at shifting them; and in particular Ellipses (and Circles which are also Ellipses). The basic ellipse and circle equations that I derived in my earlier videos are: x2/a2 + y2/b2 = 1 for ellipses and x2 + y2 = r2 for circles with a = b = r; and are centered about the origin (0 , 0). But if we were to shift this so that the center is at a point (h , k), then what we actually end up having is x replaced with (x – h) and y replaced with (y – k). When we do this replacement we can see that in order to obtain the same shape as before we have to shift each point by h in the x-direction and by k in the y-direction. I graphically show that this is the case and thus the resulting ellipse formula is (x – h)2/a2 + (y – k)2/b2 = 1. This is a very good video in understanding how to shift and move around functions graphically so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5NDuAuW2S7-z5mw1w
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-ellipses-and-circles
Related Videos:
Equation of a Circle and it's proof: http://youtu.be/xMXYJ9UeF4I
Conic Sections: Hyperbolas: Example 2: Vertical Hyperbola: https://youtu.be/zBNSTkoEzFI
Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U
Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE
Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M
Hyperbola - Definition and derivation of the equation: x2/a2 - y2/b2 = 1: http://youtu.be/Y6iYC4VEAi0
Hyperbola Examples: http://youtu.be/LvccUMFrY3k .
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▶️ 3Speak
I don't always derive the hyperbola but when I do I usually go over some extensive algebra in the derivation similar to my earlier video on ellipses ;)
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/conic-sections-hyperbola-definition-and-formula