Find an approximate polar equation for the ellipticalorbit of the earth around the sun (at one focus) giventhat the eccentricity is about  0.017 and the length of themajor axis is about 2.99 x 108 km.

Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

A: Here, given equation is x2+(y+7)2=49 By substituting x = r cos theta and y = r sin theta By…

Q: Find the eccentricity, identify the conic, and equation of the directrix. 1 r = 2 + sin 0

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Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

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Q: (c) Starting with the standard equation for this ellipse in rectangular coordinates, convert to…

A: Given ellipse is centered at origin and have length of horizontal axis is 2a and length of vertical…

Q: Find all the polar coordinates of the point P(2, p>6)?

A: Consider the given point P2 , π6

Q: Give two other polar coordinates for the point (2,pi/4). Make sure one has a positive radius and the…

A: Given, r, θ=2, π4 To find other two polar coordinates. Here,r=2 and θ=π4

Q: Given the polar equation of the conic with focus at the origin, identify the eccentricity and…

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Q: The polar equation for the curve whose rectangular(cartesian) equation xy = 4 is: (a)rcos@sin0 = 4…

A: Explanation of the answer is as follows

Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: Find Cartesian equations for the circles. Sketcheach circle in the coordinate plane and label it…

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Q: 1. Consider the rectangular (Cartesian) equation x? + (y – 2)² = 4. - d. Choose one point on this…

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Q: Identify the conic the polar equation represents and give the position of the directrix. 1 1-sin 0…

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Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: Find the lengths of the curves given by the polar coordinate equations r = 8 sin3 (θ/3), 0≤ θ ≤ π/4

A: Given data: The polar coordinate equation is r=8 sin3(θ/3). *The limit of the function is 0≤ θ ≤…

Q: Please help with this question

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Q: What are the polar coordinates of the point P shown below? 2 3 4

A: This question is related to coordinate systems, we will solve it using given information.

Q: Write a polar equation in rand of an ellipse with the focus at the origin, with the 8 eccentricity…

A: A polar equation  of the form r=ed1±e cosθ, r=ed1±e sin θ represents a conic with eccentricity e…

Q: Find the polar equation for a parabola with its focus at the origin and whose directrix is y = -a…

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Q: McKenna plots the following point on a polar coordinate plane, where both c and p are positive…

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Q: Q3 Write down the polar form of the equation 2 arctan(y/a)

A: convert the given equation into polar form x2+y2=e-2arctanyx

Q: . (a) Find the eccentricity and the distance from the pole to the directrix and sketch the plot in…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Q1) A) Replace the polar equation r? sin 20 = 2 by equivalent Cartesian equation. B; C) Find the…

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Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

A: Cartesian to polar: x=rcosθy=rsinθWherer2=x2+y2

Q: Consider the point 4, *), in polar coordinates. 3 This point is | units away from the pole on a…

A: Given point in polar coordinate is 4,π3.

Q: e = 2 / 3; directrix is parallel to the polar axis, 3 units above thepole.

A: Given e = 23 < 1  Hence the given conic is ellipse.

Q: - The polar curve r= 5sin e has the eccentricity

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Q: Find polar equations for the circle. Sketch eachcircle in the coordinate plane and label it with…

A: Cartesian (x, y) to polar r, θ coordinates: x=rcosθy=rsinθ

Q: Find the polar equation of the conic with focus at the origin and the given eccentricity and…

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Q: Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in…

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Q: A circle with the origin at (0, 0) with a radius of r=4. Write a polar equation:

A: Note that the equation of the circle is x-h2+y-k2=r2, where (h, k) is center and radius r. It is…

Q: 1. Find the Cartesian equation for the circle r = 3 V3 sin 0. Sketch the circle in the coordinate…

A: According to question,Given polar equation of circle,r = 33 sin θ

Q: Find the polar equation of a hyperbola with eccentricity 2, and directrix y = 5. Select the correct…

A: We have to find the polar equation of the hyperbola with eccentricity 2 and directrix y=5.

Q: Consider the polar equation of a conic. Determine the eccentricity. -5 r = 1 + cos(0) e =

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Q: Q1) Find the polar equation of the circle whose center has polar coordinates (a, 0,) and radius a.…

A: Given a polar point (a, theta 0) and radius a.

Q: Find a polar equation of the form r^2=f(θ) for the curve represented by the Cartesian equation x^2 −…

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Q: Q1// Converting r= 12 cos 0 from polar to the equation of a circle?

A: Solution is given below:

Q: The polar equation for the curve whose rectangu (a)rcos@sine =4 8. (b)r = sin 28 (c) =

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Q: Convert the following equation to polar coordinates. x= 10y? The polar form of x = 10y² is (Type an…

A: The solution is :

Q: Find a polar equation in the form r = f(8) of the hyperbola with eccentricity e = 4 such that one of…

A: One of the foci            =0,0    poleeccentricity                   = 4vertex nearest to pole =…

Q: For the given polar curve, identify the conic, find the equation of the directrix, and sketch it: r…

A: Given curve is r=53+8sinθ. To find: 1) Identify the conic.              2) Equation of the…

Q: For the given polar curve, identify the conic, find the equation of the directrix, and sketch it: r…

A: Given: The function is given as ? = ?/?+?????

Q: For the given polar curve, identify the conic, find the equation of the directrix, and sketch it: r…

A: Given polar curve r=53+8sinθ Comparing the above form to the general form: r=ed1+esinθ Here, e is…

Q: Prove that the polar equation of a planet's elliptical orbit is (1 – e²)a e cos 0' where e is the…

A: Given: eccentricity of the ellipse is e. length of major axis is 2a. let the equation of ellipse…

Q: Find the polar coordinates of a point with Cartesian coordinates (x, y) = (, -2). 9v3 Provide your…

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Q: What is the polar equivalent of the equation of a circle with center on the y- axis, radius equal to…

A: The equation of a circle with centre on y-axis and passing through origin is x-02+y-a2=a2. Expand it…

Q: The following polar equation describes a circle in rectangular coordinates: r = 14 sin 0 Locate its…

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Q: Which of these is the polar equation of a ellipse with eccentricity , and directrix æ = 5? Select…

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Q: What is the polar equation of a circle of radius a centered at the origin? Use this equation to…

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Q: Find a polar equation for the curve represented by the given Cartesian equation. 9. a? + y? = 25

A: Given equation x2 + y2 = 25 To be found : Polar form.of given equation.

Q: Identify the conic with a focus at the origin, and then give the directrix and eccentricity. (Use…

A: r=93+2cosθ  Rearranging this, we get  r=931+23cosθ    r=31+23cosθ

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.