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I have been spending a few days reviewing parts of College Algebra from College Algebra, by Aufmann, Barker, & Nation. I am following the discussion of the shape, features, and equation for an ellipse, and I understand the derivation well, EXCEPT that I do not know how the subsitution of b2 = a2 - c2, where a is half the length of the major axis, b is half the length of the minor axis, and c is the length from the origin to either focus. The standard form for the ellipse being:
[itex]\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/itex]
I tried drawing my own pictures, graphs, to figure out how the substitution was chosen, but I made no progress, although I see that the substituion works by just trusting it. The page in the book for this is 311 and 312.
This is NOT homework. I earned my credit in Pre-Calculus in college about three decades ago.
(This is my third edit. Sometimes the TEX equation works, sometimes the TEX equation stays with all the tags showing. This is inconsistant.)
[itex]\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/itex]
I tried drawing my own pictures, graphs, to figure out how the substitution was chosen, but I made no progress, although I see that the substituion works by just trusting it. The page in the book for this is 311 and 312.
This is NOT homework. I earned my credit in Pre-Calculus in college about three decades ago.
(This is my third edit. Sometimes the TEX equation works, sometimes the TEX equation stays with all the tags showing. This is inconsistant.)
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