Unformatted text preview: y = −d. • the graph of r = ed
1+e sin(θ) is the graph of a conic section with directrix y = d. In each case above, (0, 0) is a focus of the conic and the number e is the eccentricity of the conic.
• If 0 < e < 1, the graph is an ellipse whose major axis has length
has length √2ede2
1− 2ed
1−e2 and whose minor axis • If e = 1, the graph is a parabola whose focal diameter is 2d.
• If e > 1, the graph is a hyperbola whose transverse axis has length
axis has length √2ed 1 .
e2 − 2ed
e2 −1 and whose conjugate We test out Theorem 11.12 in the next example.
Example 11.6.4. Sketch the graphs of the following equations.
1. r = 4
1 − sin(θ) 2. r = 12
3 − cos(θ) 3. r = 6
1 + 2 sin(θ) Solution.
4
1. From r = 1−sin(θ) , we ﬁrst note e = 1 which means we have a parabola on our hands. Since
ed = 4, we have d = 4 and considering the form of the equation, this puts the directrix
at y = −4. Since the focus is at (0, 0), we know that the vertex is located at the point
(in rectangular coor...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details