Nabil is writing a science fiction novel that takes place in another galaxy. In her galaxy, all the planets travel in an elliptical orbit around their star. The majority of the plot of Nabil's story takes place on the planet Tanus which orbits a star named Ini. The length of Tanus' major axis is 150 million miles and the length of its minor axis is 75 million miles. The star Ini is located at a focus of the elliptical orbit. Use what you know about writing and graphing the equations of ellipses to answer the questions below. 1. Write an equation that models the movement of Tanus around its star. Explain how determined your equation and show you your work.

Q: ...***... .. . .. The area of an ellipse with axes of length 2a and 2b is nab. The percent change in…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the equation of the Hyperbola whose Foci are at (6,4) and ( 30,4),and the length of its…

A:

Q: (2- 8)2 (y - 5)2 = 1 81 16 Distance from the center to each focus is:

A:

Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: A sealed-beam headlight is in the shape of a paraboloid of revolution (parabolic shaped). The bulb,…

A:

Q: Graph the line and conic section. r = 4 sec (u + pi/6)

A: General equation of a line is given as y = mx + c, where m is the slope of line and c is the…

Q: Find the equation of the parabola with a focus at (1, -8) and a vertex at (1, - 2). Let a represent…

A: Since the x-coordinates of the vertex and focus are the same, they are one of top of the other. So,…

Q: Find the largest and smallest values that the function ƒ(x, y) = xy takes on the ellipse x2/8 + y2/2…

A:

Q: Determine the equation of the directrix of the curve 3x=2y2-4y+7 a. x=30/20 b. x=30/24…

A: Solution: The given equation is 3x=2y2-4y+7

Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

A:

Q: at

A: Given focus (-5,7) Directrix x=1

Q: In which direction do the following parabolas open?a. y2 = -4x        b. x2 = 4y

A: Part(a) Given parabola  The graph of the given parabola is

Q: the points where the curve meets the axes.

A: y= (x-2)(x+1)(x+2) When x=0, y=-4 When x=1, y=-6 When x=-1, y=0 When x=2, y=0 When x=-2, y=0 When…

Q: ngent to the y axis and the center is

A: To determine the circle of equation tangent to y axis and center (5,8)

Q: Find the linear speed of the moon if the average distance between the earth and moon is 239,000…

A:

Q: Jim, standing at one focus of a whispering gallery,is 6 feet from the nearest wall.His friend is…

A: Given: Jim is standing at the focus of a whimpering gallery is 6 feet. His friend is standing at the…

Q: Explain how to use directrix. ey = &x to find the parabola's focus and

A: Given equation of parabola is y2=8x. To find focus and directrix of parabola. Solution: Equation of…

Q: Distance from the center to each focus is:  (x+5)^2 - [((y-2)^2)/64] = 1

A: Topic = Hyperbola

Q: A planetary orbit can be expressed by the equation %3D 3249 = 1. What is the 3600 length of the…

A: Given the equation of an planetary orbit as x23600+y23249=1

Q: Based on the view from above, write an equation describing Han's vertical position v, in feet,…

A: In this question, the concept of a trigonometric function is applied. Trigonometric Function The…

Q: Find the equation of the parabola with focus at (5, 0) and directrix x = −5.

A: Focus lies on x-axis.

Q: Given the following conic section, determine its shape and then sketch its graph. 5x? + 4y? + 3x +…

A:

Q: Determine the coordinate of a 3D point (100.0, 29.0, -79.5) after rotating 60° across Y-axis, given…

A: Given:                       point: A100.0,29.0,-79.5                Rotation: θ = 60° across…

Q: A satellite is in elliptical orbit around the earth with the center of the earth at one focus. The…

A:

Q: Whispering Gallery Jim, standing at one focus of awhispering gallery, is 6 feet from the nearest…

A: Ellipse is a closed circle that looks like an elongated circle. ellipse contains focus, major axis,…

Q: The planets have elliptical orbits with the Sun as one of the foci, Pluto (orange), the planet…

A: Given the length of the semimajor axis 2a=11827×106km. The distance from pluto to the sun is…

Q: (x – 6)? (y + 4)² = 1 9. 25 Distance from the center to each focus is:

A:

Q: .... .. ......... ....*.*. ..* * ..... The area of an ellipse with axes of length 2a and 2b is nab.…

A: As per our guidelines , we can only solve first question. Please resubmit other questions as next…

Q: |xy dA, D is enclosed by the quarter-circle 20. y - 1 - x² , x > 0, and the axes

A:

Q: which conic was Euclid's favorite and why?

A: The four types of conic sections are a. Ellipse b. Parabola c. Hyperbola d. Circle

Q: Determine the equation of the directrix of the curve 3x=2y2-4y+7 (Graph Solution) a. x=30/20…

A:

Q: Leigh and David are playing a game of laser tagʻ. David has managed to climb aboard a mining cart…

A: (a) Leigh travels along the xAxis with the velocity v at the time s. We know that,…

Q: Eliminate the parameter to find a Cartesian equation of the curve.

A: Given  x=sin(t)  y=csc(t) and 0<t<π/2 We need to find the Cartesian equation and graph

Q: The Ferris wheel below has a radius of 32 feet, a center height of 50 feet, and makes a full…

A: Radius of the Ferris wheel:= 32 feet;                    Center height of the…

Q: Leigh and David are playing a game of laser tag'. David has managed to climb aboard a mining cart…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: ^2+84x-24y

A: Given Ellipse: 21x2-4y2+84x-24y=36This equation can be re-written as-21(x2+4x)-4(y2+6y)=36 To find…

Q: Graph the curve whose parametric representation is given. x-iy-4t + 3; 0sts4 B) D) 10- -10

A: we have to draw the graph of given parametric equation

Q: x+4 5 y-2 -5 2+1 1

A: Given the equation is x+45=y-2-5=z+11

Q: Q11

A: Just join the centres of two parabolas and draw a line joining them, it is called transverse axis.…

Q: Identify this conic, list the necessary parts and then graph it: 2x2 +2y2 +8x=7

A: Given the equation of conic

Q: The device is a parabolic dish with a sound booster at its focus. The device is 6ft across and 20…

A: This question is based on parabolic equation.

Q: Find the equation of the following conic in GENERAL form. 1. Circle that is tangent to the lines…

A: Consider the equation of the circle is x-h2+y-k2=r2 where h, k is the centre and r is radius. It is…

Q: Reflect Point C over the y-axis: A 3 -5 -4 -3 -2 -1 5 -1 O a) (-3, 2) O b) (3,2) O d) (3,0) c)…

A:

Q: 4- Sketch the curve 9x + 16y = 144.

A:

Q: Find the equation of the family of circles whose center is at the y-axis. A. y "+ 3y + 7 = 0 В. ху "…

A: Please refer the attached image for complete solution.

Q: The earth moves in an elliptic orbit about the sun, with the sun at one focus. The least and…

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

Q: Below is the equation of a conic section such that the ordered pair (Fx, Fy) corresponds to its…

A:

Q: find a cartesian equation for the curve r=3cos(θ)

A: Cartesian equation for the curve is r=3 cos(θ)   Now x=r cos(θ)  …….. equation(1) cosθ=xrr=3xcosθ…

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.