An ellipse is the collection of all points in the plane such that the sum of the distances from two fixed points, each called a focus, is constant. See the illustration below'. The foci are depicted using the notation F1 and F2. The line containing the foci is called the major axis. Major axis Recall that the equation of an ellipse centered at the origin may be written in two different ways depending on whether the major axis is the x- or y-axis: Major axis is the x-axis²: Equation of an Ellipse: Center at (0, 0); Major Axis along the x-Axis An equation of the ellipse with center at (0,0), foci at (-c, 0) and (c.0), and vertices at (-a, 0) and (a, 0) is where a > > 0 and b²=a²² The major axis is the x-axis. See Figure 19. V₁-(-a, 0) (0. 5-(-20) (c) (0-0) ½-(40) (2) 1 Sullivan & Sullivan, Precalculus: Concepts Through Functions: A Unit Circle Approach to Trigonometry, 3rd ed. p. 670 2 Sullivan p. 671 1 2. The orbit of the Hale-Bopp comet around the Sun can be modeled as parabolic orbit or elliptical orbit. For the purposes of this exercise, we assume that the orbit is elliptical. Use the characteristics of the Hale-Bopp comet to find an equation of the ellipse that models its orbit around the Sun. Use the origin as the center and the x-axis as the major axis. Refer to the examples on the previous page. Clearly indicate the units, e.g. AU, millions of miles etc.
An ellipse is the collection of all points in the plane such that the sum of the distances from two fixed points, each called a focus, is constant. See the illustration below'. The foci are depicted using the notation F1 and F2. The line containing the foci is called the major axis. Major axis Recall that the equation of an ellipse centered at the origin may be written in two different ways depending on whether the major axis is the x- or y-axis: Major axis is the x-axis²: Equation of an Ellipse: Center at (0, 0); Major Axis along the x-Axis An equation of the ellipse with center at (0,0), foci at (-c, 0) and (c.0), and vertices at (-a, 0) and (a, 0) is where a > > 0 and b²=a²² The major axis is the x-axis. See Figure 19. V₁-(-a, 0) (0. 5-(-20) (c) (0-0) ½-(40) (2) 1 Sullivan & Sullivan, Precalculus: Concepts Through Functions: A Unit Circle Approach to Trigonometry, 3rd ed. p. 670 2 Sullivan p. 671 1 2. The orbit of the Hale-Bopp comet around the Sun can be modeled as parabolic orbit or elliptical orbit. For the purposes of this exercise, we assume that the orbit is elliptical. Use the characteristics of the Hale-Bopp comet to find an equation of the ellipse that models its orbit around the Sun. Use the origin as the center and the x-axis as the major axis. Refer to the examples on the previous page. Clearly indicate the units, e.g. AU, millions of miles etc.
Chapter11: Conics
Section11.3: Ellipses
Problem 11.51TI: A planet moves in an elliptical orbit around its sun. The closest the planet gets to the sun is...
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I need help with this question https://www.spacereference.org/comet/c-1995-o1-hale-bopp
This is where I got my perihelion and eccentricity of orbit but my orbital period is 2,534 years.
Transcribed Image Text:An ellipse is the collection of all points in the plane such that the sum of the distances from two
fixed points, each called a focus, is constant. See the illustration below'. The foci are depicted
using the notation F1 and F2. The line containing the foci is called the major axis.
Major axis
Recall that the equation of an ellipse centered at the origin may be
written in two different ways depending on whether the major axis is the x- or y-axis:
Major axis is the x-axis²:
Equation of an Ellipse: Center at (0, 0); Major Axis along the x-Axis
An equation of the ellipse with center at (0,0), foci at (-c, 0) and (c.0), and
vertices at (-a, 0) and (a, 0) is
where a > > 0 and b²=a²²
The major axis is the x-axis. See Figure 19.
V₁-(-a, 0)
(0.
5-(-20) (c)
(0-0)
½-(40)
(2)
1 Sullivan & Sullivan, Precalculus: Concepts Through Functions: A Unit Circle Approach to Trigonometry, 3rd ed. p. 670
2 Sullivan p. 671
1
Transcribed Image Text:2. The orbit of the Hale-Bopp comet around the Sun can be modeled as parabolic orbit or elliptical
orbit. For the purposes of this exercise, we assume that the orbit is elliptical. Use the
characteristics of the Hale-Bopp comet to find an equation of the ellipse that models its orbit
around the Sun. Use the origin as the center and the x-axis as the major axis. Refer to the
examples on the previous page. Clearly indicate the units, e.g. AU, millions of miles etc.
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