Stitz-Zeager_College_Algebra_e-book

Stitz-Zeager_College_Algebra_e-book

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the center to a vertex In an ellipse, the foci are closer to the center than the vertices, so 0 < e < 1. For the ellipse above on the left, e ≈ 0.98; for the ellipse on the right, e ≈ 0.66. In general, the closer the eccentricity is to 0, the more ‘circular’ the ellipse; the closer the eccentricity is to 1, the more ‘eccentric’ the ellipse. 426 Hooked on Conics 1 Example 7.4.4. Find the equation of the ellipse whose vertices are (0, ±5) with eccentricity e = 4 . Solution. As before, we plot the data given to us y x From this sketch, we know that the major axis is vertical, meaning b > a. With the vertices located at (0, ±5), we get b = 5 so b2 = 25. We also know that the center is (0, 0) because the center is the midpoint of the vertices. All that remains is to find a2 . To that end, we use the fact that the 1 eccentricity e = 4 which means distance from the center to a focus c c 1 === distance from the center to a vertex b 5 4 √ 5 from which we get c = 4 . To get a2 , we use the fact that c = b2 − a2 e= 5 4 √ c= b2 − a2 √ 5 25 −...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online