The latitude and longitude of a point in the Northern Hemisphere are related to spherical coordinates , , as follows. We take the origin to be the center of the earth and the positive -axis to pass through the North Pole. The positive -axis passes through the point where the prime meridian (the meridian through Greenwich, England) intersects the equator. Then the latitude of is and the longitude is . Find the great-circle distance from Los Angeles (lat. N, long. W) to Montréal (lat. N, long. W). Take the radius of the earth to be 3960 mi. (A great circle is the circle of intersection of a sphere and a plane through the center of the sphere.)

Q: The center of a circle of radius 3 inches is at a distance of 20 inches from the center of a circle…

A: Given that, OA = 3 inches PB = 9 inches  OP = 20 inches

Q: Find the length and area of the sector whose central angle is e = 40° and radius is 2. 500 cm.

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Q: The circle x² + (? − 1) 2 = 1 is rotated around the line y = x-3. A torus is formed as a result of…

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Q: 1. Two gears of radii 2.5 cm and 4.8 cm are adjusted so that the smaller gear drives 0O arger one,…

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Q: For the spherical object shown next described as 3<r<6, 65°<0<95° , 50°<p<80° The length of the…

A: To find: The length of the segment AE. Given information: 3&lt;r&lt;6, 65°&lt;θ&lt;95°,…

Q: Find the area of a sector of a circle with central angle 2T/3 if the radius of the circle is 4cm. O…

A: A sector with central angle 2π3 and the radius of the circle is 4 cm.

Q: Convert to polor coordinates with  r ≥ 0 and 0 ≤ theta < 2pi (4,0)  (r, theta) = ?

A: Polar coordinates (r, θ)            where r ≥ 0 and 0 ≤ theta &lt; 2pi Cartesian coordinates (x, y)…

Q: In a right spherical triangle LMN, N is the 90°. Given that side MN is 134° and side LN is 44°, in…

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Q: A point is rotating with uniform circular motion on a circle of radius r. Find ? if r = 10 cm and v…

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Q: A is approximately due north of B. The latitude of A is 480N while the latitude of B is 300 N (N-…

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Q: 13. Lincoln, Nebraska (40.8° N, 96.7° W) and Dallas, Texas (32.8° N, 96.7° W) have approximately the…

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Q: Express the circle specified by ?=2cos(?)?=1+2sin(?) y=1+2 sin(?) inin Cartesian coordinates and…

A: Equation of a circle with radius r and center (h,k) is  (x-h)^2 + (y-k)^2  = r^2

Q: A ship sails due North from point P to point Q 4km away.It then sails on a bearing 090°(eastwards)…

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Q: A graphic designer created a prellminary sketch for a company logo. In the figure, BC and CD are…

A: ABCD is a Irregular Polygon Defination of Irregular Polygon  -                 Any polygon that is…

Q: Find the distance between the driven and the sink, determine whether the work triangle shown is…

A: To find- Distance between sink and stove, if the traingle  used is right angled, acute or obtuse and…

Q: Solve for the spherical triangles given the following parts. 1.A = 73045' C = 100°07' %3D c = 900 2…

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Q: In triangle ABC, AB = 15 cm., BC = 18 cm. and CA = 24 cm. If the area of the triangle is equal to…

A: If S is the the semiperimeter of the triangle  and r is he radius of inner circle of triangle , then…

Q: 14. Find the area of the sector with radius of 8 feet and an angle 57 of O 44.43 ft2 O 125.664 ft2 O…

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Q: Solve for the remaining parts of a right spherical triangle given the following parts. 1.] b =71°53'…

A: Solution is here   Rules: Rule 1: The SINe of a missing part is equal to the product of the TAngents…

Q: If T is the point at a distance T from P(1, 0) on the unit circle with its center at (0, 0), in what…

A: T is the point at the distance of 5π4 in the unit circle.To find the point.

Q: At the Maryland State Fair, there Is a zoom in with the following dimensions: • Radius 30 ft •…

A: According to our guidelines I am answering first three subparts. Please resubmit other parts in…

Q: Find the center of the circle having the radius= 20 units and the points on the circumference of the…

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Q: On the unit circle, the terminal side of angle 0 intersects the circle at a point (x, y). If 0 is…

A: We have to find the co-ordinates of the terminal point (x,y) if an angle θ = 120° intersects a unit…

Q: - In the acute- angled triangle OPQ, the altitude OR makes angles A and B with OP and OQ. Show by…

A: Our objective is to prove  p. q. Sin(A+B) =q.r.SinA+ p.r.Sin B

Q: The three circles are arranged so that they touch each other, as shown in the figure. Use the given…

A: Three circles with radii 5, 4.3, and 3.1 cm respectively are arranged so that they touch each other.…

Q: the law of sine for plane triangles given by All of the above is true .I O sina/a sine/b sing/c .I O…

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Q: If T is the point at a distance T from P(1, 0) on the unit circle with its center at (0, 0), in what…

A: Given :- unit circle with centre (0,0)

Q: Determine the area of a spherical triangle ABC if A = 120", B = 85° and C = 76', if it has a radius…

A: We have to find the area of the given spherical triangle.

Q: Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and that…

A: distance between two location having latitude in radians (Max rad. - Min rad.)*radius of the earth

Q: Find the distance l along the surface of the earth between City A and City B if the two cities…

A: Given  Central angle determine by City A and City B = 36.65⁰ Radius of earth = 4000km

Q: In circle A, BC is tangent to the circle. А C. 3. If the distance of point C from the center of the…

A: Given

Q: Find the area of a sector with a central angle of 75° and a radius of 12 cm. Leave answer in terms…

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Q: 10. In circle A as shown below, segment DC is tangent to circle A at D. Also, DC= 4 and BC= 2. A B.…

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Q: An engineer wants to construct an elliptical driveway with a major axis of 60 km and a minor axis of…

A: Ellipse

Q: If the relation between the spherical coordinates ' and the rectangular Cartesian coordinates x is…

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Q: The three shown circles, with radius 15 in., 10.5 in., and 4.5 in., are tangent to each other. (a)…

A: c=15+10.5=25.5b=15+4.5  =19.5a=10.5+4.5=15a) from law of cosine c2=a2+b2-2ab cos γ…

Q: A boat sails 160 km from a harbour P on a bearing of 036° to Q and then 200 km on a bearing of 125°…

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Q: Given the spherical triangle AABC whose sides have measure a, b, c as indicated. Use three…

A: Given:

Q: Two boats are traveling toward a lighthouse that is 200 feet (ft) above sea level at its top. When…

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Q: If a point on the Cartesian plane lies at (4, 2), what is the angle made between the line containing…

A: Using the given information, draw a figure and label it. We need to find the value of α i.e., 90+θ…

Q: Find the missing parts of the right spherical triangle, given a = 22°; A = 62°.

A: Given

Q: A sector of a circle has a central angle of 45°. Find the area of the sector if the radius of the…

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Q: 1. In the example above, what is the height of the tunnel 12 ft away from the center towards the…

A: From the  example above,                                      We can see that we are using the…

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 2000 feet apart. As the…

A: Given that the total length XY = L = 2000 feet and the angle A = 40 degree and angle B = 20 degree.…

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L= 1850 feet apart. As the…

A: SOLUTION-

Q: A fheld is in the form of a regular pentagon. The direction of the bounding sides was surveyed with…

A: Given that, A field is in the form of a regular pentagon. Bounding sides surveyed with assumed…

Q: The sides of a triangle are 7 m, 9 m, and 11 m, respectively. Find the radius, in m, of the circle…

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Q: 4* Find the perimeter of a sector of a circle with central angle = 3 16 b) 0 (4+1) O c) 08 ft d) 0…

A: Given :Radius r= 4 ftCentral angle θ = 4π3

Q: Find area of a sector of a circle of diameter 20 centimeters with central angle of 60. What is the…

A: Diameter=20 cm⇒radius=10 cm    ∵Diameter=2×radius&amp; θ=60°=π3 The diagrammatic representation is,

Q: The distances between the centers of the 3 circles which are tangent to each other externally are…

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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.