The distance from the planet Pluto to the Sun is 4.43 x 10° km at perihelion and 7.37 x 10 km at aphelion. Find the eccentricity of Pluto's orbit.

Q: Find a polar equation for the circle x2 + ( y - 3)2 = 9

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Q: Suppose a baseball is thrown at 30 ft/s at a 60degree angle to the  horizontal from a height of 4 ft…

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Q: The propellers for a toy boat are manufactured by stamping out a rose with n petals and then bending…

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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: Find the polar coordinates of a point with the following cartesian coordinates.

A: to find:- polar coordinate.

Q: Find the polar form of 1 + sqrt(3i)

A: Find the Polar form of complex number  Given z = 1 + √3i

Q: find the eccentricity, identify the conic, give an equation of the directrix and sketch the graph of…

A: Solution is given below:

Q: convert the polar equation to a cartesian equation rcos(θ+(π/6))=1

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Q: Find the polar coordinates for each point. (1, –1)

A: Let the polar coordinates of (1, -1) = r,θ It is given that…

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

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Q: Consider the spherical equation given by p = 4 cos 0 sin $. Determine its corresponding equation in…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: What is the reason that degrees is used rather than radians in a spherical coordinate system?

A: Solution: We have given that spherical coordinate system and have been asking that the reason behind…

Q: ven in polar coordinates.

A: The polar coordinates (r,θ)and rectangular coordinates (x,y)where x=r cos θ         y=r sin θx=2 cos…

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Above question is solved.

Q: State the formulas for converting rectangular to spherical coordinates.

A: Converting rectangular to spherical coordinates.

Q: Which quadrant will the figure be located in after a 180 degree rotation? 2 3 -4 G O Quadrant 1 O…

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Q: Plot the polar point ( 4, 330° ). (Click on the purple dot and move it to the desired location.)

A: To plot the polar point (4,330∘).

Q: Find an approximate polar equation for the ellipticalorbit of the earth around the sun (at one…

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Q: A horizontal bridge is in the shape of a parabolic arch.Given the information shown in the figure,…

A: A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure…

Q: The orbit of Mars around the sun is an ellipse with eccentricity 0.093 and semimajor axis 2.28 x 108…

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Q: Convert to polar equation. Express rinterms of Q 4x + y = 5

A: The objective is to convert in terms of polar equation.

Q: Find the directrix of the parabola r = 25/(10 + 10 cos θ)

A: The parabola r=2510+10cosθ, we have to find the directrix of this given parabola.

Q: 2) 180 rotation

A: Explanation of the answer is as follows

Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given surface in spherical co-ordinate system is ρ=sin Φ sin θ     .......(1)

Q: The orbit of Mars around the sun is an ellipse with eccentricity 0.093 and semimajor axis 2.28 × 108…

A: We know that polar equation of ellipse with focus at origin, semi major axis a and eccentricity e…

Q: Cannot solve

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Q: Give four different pairs of coordinates for the point shown on the polar grid

A: The solution is :

Q: Find a polar equation for the line containing the origin that makes an angle of 30° with the…

A: Find a polar equation.

Q: Identify the conic that each polar equation represents.Also,give the position of the directrix.

A: A conic section is obtained from the intersection of a plane with surface of a cone. Three types of…

Q: Plot the point whose polar coordinates are (5, 135°).

A: Plot the polar coordinate as follows.

Q: The planet Saturn orbits the Sun in an elliptical path with the Sun at one focus. The eccentricity…

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

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: convert the given polar equation to a Cartesian equation. Write in the standard form of a conic if…

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Q: Eliminate the parameter, An ellipse: x = h + a cos t, y = k + b sin t. Write the resulting equation…

A: Let's consider the given equations for the ellipse:…

Q: Write the equation for the ellipse rotatedπ6 radian clockwise from the ellipse r = 8/(8 + 5 cos) .

A: Given the equNoNow, When wation of the ellipse: r=88+5 cosθ

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: Please help me solve

A: Given the function y = f(x)

Q: Of a circle of radius "a" whose center is point (1,-1).Write the equation in Polar Coordinates.…

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Q: Find parametric equations for the circle with center(h,k) and radius .

A: Find parametric equations for the circle with center(h,k) and radius r.

Q: Find the rectangular coordinates for the point whose polar coordinates are 五-4

A: Cos x =x/r Sin x= y/r

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: The Hale-Bopp comet, discovered in $1995,$ has an elliptical orbit with eccentricity 0.9951 and the…

A:

Q: 6. Find the area of an ellipse, using the cartesian equation; check by using the equations z= a cos…

A: we have to find area

Q: Find the polar equation of the elliptical orbit of the planet Saturn and the perihelion a = 1.434 ×…

A: The polar equation of the elliptical orbit is r=(1-e2)a1-ecosθ, where e is the eccentricity, the…

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

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Q: Find a polar form of the equation. x² + y2 = 49

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Q: Convert the equation x2 + y2 = 1 to spherical coordinates and write in standard form, solving for ρ

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Q: Find the polar equation of the elliptical orbit of the planet Neptune and the perihelion a = 4.495 ×…

A: The formula of the polar equation of the elliptical orbit is, r=1-e2a1-ecosθ where a is major axis…

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.