The Purplemath Forums

by **jumicox70** on Tue Mar 10, 2009 3:23 pm

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

**Sponsor**

by **stapel_eliz** on Tue Mar 10, 2009 5:56 pm

jumicox70 wrote: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!

The Purplemath Forums

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

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