ss_9_3

ss_9_3 - Section 9.3 The Ellipse Recall that an ellipse can...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 9.3 The Ellipse Recall that an ellipse can be obtained as the graph of the quadratic equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 with discriminant B 2 - 4 AC < 0. An alternate method for obtaining an ellipse is given by the following definition. Let F 1 and F 2 be any two distinct points in the plane. An ellipse is the set of all points P in the plane such that d ( P, F 1 )+ d ( P, F 2 ) = constant, where d ( A, B ) denotes the distance from A to B. The points F 1 and F 2 are called the foci of the ellipse. The graph of an ellipse is shown below. In the above figure, the points V 1 and V 2 are called vertices of the ellipse. The line segment between V 1 and V 2 is called the major axis . The line segment through the center of the ellipse and perpendicular to the major axis is called the minor axis . The equation of an ellipse is much simpler when its major axis is either horizontal or vertical. Ellipses centered at the origin and having horizontal and vertical axes are shown below. Note in these diagrams the relationship between the distances a , b ,and c . The number a is half the length of the major axis, the number b is half the length of the minor axis, and the number c is half the distance between the foci. Hence, a>b a>c .Ineachcase a 2 = b 2 + c 2 . x 2 a 2 + y 2 b 2 =1 y 2 a 2 + x 2 b 2 Remark. In the equation x 2 r 2 + y 2 s 2 = 1, the larger of r, s is the number a and the smaller of r, s is the number b . The larger of the two numbers r , s determines whether the major axis is either horizontal or vertical.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

Page1 / 5

ss_9_3 - Section 9.3 The Ellipse Recall that an ellipse can...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online