## Eccentricity of an ellipse: 16x^2 + 25y^2 = 100

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
jumicox70
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### Eccentricity of an ellipse: 16x^2 + 25y^2 = 100

How do I find the eccentricity of the ellipse given by 16x^2+25y^2=100?

stapel_eliz
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How do I find the eccentricity of the ellipse given by 16x^2+25y^2=100?
First, you'd convert the ellipse equation into conics form. In this case, you don't have to complete the square; you only need to divide through by 100 to get the equation into "=1" form.

. . . . .$\frac{16x^2}{100}\, +\, \frac{25y^2}{100}\, =\, \frac{100}{100}$

. . . . .$\frac{4x^2}{25}\, +\, \frac{y^2}{4}\, =\, 1$

. . . . .$\frac{x^2}{\left(\frac{25}{4}\right)}\, +\, \frac{y^2}{2^2}\, =\, 1$

. . . . .$\frac{x^2}{\left(\frac{5}{2}\right)^2}\, +\, \frac{y^2}{2^2}\, =\, 1$

Then use what you know about the values of "a" and "b" (in the denominators), along with the formulas relating "a", "b", and "c", to find the value of "c", and thus to find the value of the eccentricity e = c/a. (The lesson in the link provides worked examples, too.)

If you get stuck, please reply showing how far you have gotten. Thank you!