The orbit of Halley's comet, last seen in 1986 and due to return in $2062,$ is an ellipse with eccentricity 0.97 and one focus at the sun. The length of its major axis is 36.18 AU. [An astronomical unit (AU) is the mean distance between the earth and the sun, about 93 million miles.] Find a polar equation for the orbit of Halley's comet. What is the maximum distance from the comet to the sun?

Q: The surface of equation= ++ = 1 is: - 4 16 An ellipsoid A circular cylinder A cone A sphere

A: Equation of ellipsoid

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A: x=h+asect , y=k+btant On simplification, we get ⇒asect=x-h , btant=y-k⇒sect=x-ha , tant=y-kb

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A:

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A:

Q: Let a, b > 0. (a) Calculate the area inside the ellipse given by the equation 1. 62 || a²

A:

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A: We have to find percent change in the area after increasing major axis and minor axis.

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A:

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A: answer is in next step

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A: We have to find a Cartesian equation for this curve and sketch the parametric curve.

Q: 5. Trace the curve r = sinecos³e.

A: To find the trace of the given curve r=12sinθcos3θ

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A:

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A: Given the vertex is at(0,0) and focus (3, 0)

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A: Here we have a major axis of ellipse 2a= 44.6 cm and minor axis of ellipse = 2b= 29 cm

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A: The radius of a mixing blade on a food processor is 3 inches from the center. The blade is turning…

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A:

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A: Given: Length of the major axis is 2a=768,800 km Thus,  a=768,8002=384,400 km Length of the minor…

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A: It is given that the eccentricity of the orbit is 0.0565 and the distance between the sun and Saturn…

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A: To find the slope we first need dy/dx This is the slope.

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A: You can find in the following way:-

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A:

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A: consider (x0 ,y0) be an any point on ellipse

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A: Solve for the maximum distance between the satellite and the centre of the planet

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A: Question is solved.

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A: For the solution follow the next step.

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A:

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A: Consider the eccentricity for the satellite orbit.                     e=A-PA+P     ..............1…

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A: Differentiating with respect to x, we get Now slope of the normal is,

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A:

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A:

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A: The standard equation for the ellipse is x2a2+y2b2=1. Here, a is the length of the semimajor axis…

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A: According to question We have to calculate an equation to represent the orbit of plutoAround the…

Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. 3 4x + y…

A:

Q: The surface of equation + 1 is: 16 A circular cylinder An ellipsoid

A: An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional…

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A: The explanation of the solution as follows:

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A: Given that Jupiter is closest to the sun at 7.4052×108 km and eccentricity of the orbit is 0.0489.

Q: Question 6 Find the tangent line to the ellipse 1 at the point (xo, yo).

A: I have appended the formula used in the solution part.

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A: It is given that the orbits Halley’s comet and the comet Hale Bopp orbit the sun in the elliptical…

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A: Given : The first artificial satellite earth was sputnik I. its highest point above the earth's…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.