The apogee (the point in orbit farthest from Earth) and the perigee (the point in orbit closest to Earth) of an elliptical orbit of an Earth satellite are given by A and P, respectively. Show that the eccentricity of the orbit is                              e =( A − P)/( A + P).

Q: C. A man, of height 1.75m, stands on top of a building of height 52m and looks at a car at an angle…

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Q: Deduce from the orbit equation (1 + e)r 1 + e cos 0 that a planet is closest to its sun when 0 = 0…

A: Here,  r=(1+e)r01+ecosθ differentiate with respect to θ

Q: Consider the following. x = sin(t),    y = csc(t),    0 < t < π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

Q: Find the arc length of the graph of the given equation from A to y = 6x2/3 + 1 А(-1,7), В(—8,25) B.

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Q: Suppose an object moves in an elliptical orbit parametrized byx = 4 cos t and y = 7 sin t, where t ≥…

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Q: A satellite is in an elliptical orbit around the earth with the center of the earth at one focus, as…

A: Suppose that major axis of elliptical orbit is x-axis. Then, 2a=440+2r+120. Here, a is the length of…

Q: Find the lengths of the curves The parabolic segment r = 6/(1 + cos θ), 0 ≤ θ ≤ π/2

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Q: The graph of an equation of the form r = au, where a is a nonzero constant, is called an Archimedes…

A: Given the graph of the equation of the form r=au called Archimedes spiral. We need to find the is…

Q: = L

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Q: Find the lengths of the curves The curve r = cos3 (θ/3), 0 ≤ θ ≤ π/4

A: Now,

Q: Find the arc length of the asteroid x2/3 + y2/3 = 32/3.

A: Given curve is

Q: Make a sketch to illustrate the bearing starting from the origin in the center. N71°E -וייויק

A: The objective is to make a sketch illustrate the bearing starting from the origin in the centre.

Q: 29 In the figure, the tangent to the circle at T cuts a chord AB produced at C. la) Prove that ATBC…

A: This is a problem related to the geometry side. Based on the general formula we will prove and solve…

Q: A slime mold grows in a spiral pattern with polar radius r=θ3r=θ3. If the mold grows by continuing…

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Q: Find the arc length of the asteroid x2/3+y2/3=72/3

A: We have given; x2/3+y2/3=72/3

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed insıde a smooth…

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Q: . A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

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Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of…

A: Given: r = 6 cm, v = 3 cm/sec

Q: Determine the moment of Inertia about the Y axis for the sections shown below. 20cm 5cm 15cm 5cm Scm…

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Q: Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference…

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Q: Suppose I am in a boat and I travel at the bearing N80°E at 33 knots for 5 hours. At the end of the…

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Q: Calculate the distance on the ellipsoid if the distance on the secant is 18267.46

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Q: Find the arc length of the graph of the given equation from A to B (x+3)2 = 8 (y-1)3 A(-2,3/2)…

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Q: Find the arc length of the following curve given in parametric form:

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Assume the center of the motion is the origin, the motion is counterclockwise and that t = 0…

A: This is basic equation of motion problem

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: Deduce from the orbit equation r=(1 + e)r0 /(1 + e cos u) that a planet is closest to its sun when u…

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Q: 2. Find points P and Q on the parabola y = 1 – x? so that the triangle ABC formed by the r-axis and…

A: Given:  To find points P and Q on the parabola y=1-x2 so that the triangle ABC formed by the x‐axis…

Q: QUESTION 2 The value of keid where b41 by using the two-point Gauss quadrature method of integrafion…

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Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: Find the equation of the osculating, normal, and rectifying planes for a (t) ( cos t, – sin t, cos…

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Q: Calculate the length of the astroid of a + ys = 3.

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Q: For each of the following problems, a point is rotating with uniform circular motion on acircle of…

A: Angular speed, w=linear speed,v/Radius,r

Q: a) Show that the length of the arc of parabola y? =16x measured from the vertex to an extremity of…

A: Given the parabola y2 = 16x.

Q: Consider the following. x = sin(t), y = csc(t), 0 < t < A/2 %3D %3D (a) Eliminate the parameter to…

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Q: Find the length of the curve over the given interval: r=3acos(theta) Interval: [-pi/6,pi/6]

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Q: Show that the substitution 1- x a = -1, b = l+ 1, c = 1 2 converts the hypergeometric equation into…

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Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

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Q: If the parametric curve starts at (- 2, – 9) when t = 0 and ends at (5, 7) att = 1, then find a, b,…

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Q: Calculate the length of the astroid x + y = 1 shown in the following figure. X+

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Q: Consider the following. x = sin(0.5θ),    y = cos (0.5θ),    −π ≤ θ ≤ π (a) Eliminate the parameter…

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Q: The distance from the planet Pluto to the sun is $4.43 \times 10^{9} km$ at perihelion and $7.37…

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Q: Consider the following. X = sin y = = COS (a) Eliminate the parameter to find a Cartesian equation…

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Q: of the box has a height dy. Draw the trough, the water, and the element with the distance y.

A: A 2-dimensional side view of the trough will show the length of the trough and the height of the…

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: the arclength of the curve y = on 3

A: We will solve the problem.

Q: Find the length of the arc of the parabola y sq = x cu .  from  ( 0, 0 )  to ( 1,1)

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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.

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.