y? xy ds; C is a portion of the ellipse 4 1 in the first 16 quadrant, oriented counterclockwise.

Q: Graph the ellipse 9(x - 1)2 + 4(y + 3)2 = 36 and give the location of its foci.

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Q: What are the foci of the ellipse? 49 42 O (2+ v7, 1) o (2+ 7, -1) o (tyī, 1) o (12/7, - 1)

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Q: In the equation 4x^2 + 9y^2 − 24x + 36y + 36 = 0 of an Ellipse, what is the Center, Foci, Major nad…

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Q: Find an equation for the ellipse shown in the figure.

A: Center, (h,k)=(0,0) Length of major axis, 2a=8 Length of minor axis, 2b=6

Q: Draw the ellipse 5(x − 1) 2 + 4(y − 1) 2 = 25, labeling all important information.

A:

Q: Find the equation of the ellipse obtained by translating (as indicated) the ellipse translated with…

A: The given equation is x-862+y+432=1.

Q: The equation of the ellipse that has its center at the origin with focus at (0, 4) and vertex at (0,…

A: The ellipse has its center at the origin with focus at 0,4 and vertex at 0,7

Q: Find the equation of an ellipse whose minor axis is 6 and whose foci are located at (+8, 0). y? 9.…

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Q: 4a² + y = 4

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Q: Find the standard form of the equation of the ellipse with the given characteristics. Foci: (0,0),…

A: Since foci lie on y-axis, so the ellipse is of type where (h,k) is center of ellipse and 2a is…

Q: Write the equation of the ellipse 16x? + 9y? + 160x – 90y + 481 = 0 in standard form %3D (æ – h)? (y…

A:

Q: Find the center and foci of the ellipse. (x+5) (y+9)² = 1 %3D

A: The given ellipse equation,(x+5)25+(y+9)29=1

Q: Find an equation of the ellipse with center at (0, 0); vertex at (0, 4); focus at (0, -2).

A:

Q: 4. §yʻ dz + 2ry³ dy, where C is the ellipse z + 2y? = 2.

A: To Determine: find the integral  Given: ∮y4dx+2xy3dy where C is the ellipse x2+2y2=2 Explanation: we…

Q: (d) If x + y = xy, show that y" = . (e) Evaluate y" for the ellipse b'x? + a²y² = a²b°.

A: We have to differentiate the given expressions with respect to x.

Q: find the equation of the ellipse obtained by translating (as indicated) the ellipse(x − 8/6)2+(y +…

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Q: Sketch the graph of the ellipse with equation 9x + 4y = 36 %3D

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Q: Find an equation for the ellipse. Center at (0, 0); focus at (3, 0); vertex at (4, 0)

A: SOLUTION-

Q: Graph the ellipse (x - 3)2 + 9(y + 2)2 = 18 and give the location of its foci.

A: the given equation of ellipse is  (x-3)2+9(y+2)2=18

Q: The equation x 2 −xy +y 2 = 3 represents a rotated ellipse, that is, an ellipse wholes axes are not…

A: The given equation is: x2-xy+y2=3 Now the ellipse will cross the x-axis, when y become zero. Thus,…

Q: (b) Find the evolute of the ellipse x2 y? =D1

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Q: Write the equation of the ellipse 4x² + 25y? – 40x + 150y + 225 = 0 in standard form %3D (x – h)?,…

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Q: I. Find the standard equation of the ellipse which satisfies the given conditions. 4. covertices…

A: As per Bartley guidelines we are supposed to answer only one question per post. This post contains…

Q: Find an equation for the ellipse. Center at (0, 0); focus at (-2, 0); vertex at (7, 0)

A: According to question given that Center (0,0), focus (-2,0), vertex (7,0)We have to find the…

Q: Given the ellipse x2/36 + y2/32=1. Determine the distance between foci.

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Q: Graph the ellipse (x - 4)2/9 + (y + 2)2/25 = 1 and give the location of its foci.

A: Given: x-429 + y+2225 = 1 To find: Location of the foci and to graph the ellipse.

Q: Find the axes of this tilted ellipse 5x2 + 8xy + 5y? = 1, and sketch the graph of both ellipses.

A: Consider the general equation for the ellipse and compare the given equation to the general equation…

Q: Write the equation of the ellipse 36æ² + 4y? + 72x + 32y – 44 = 0 in standard form (x – h)? p2 (y –…

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Q: (-3x) dxtxdy C is part of the ellipse 5x2+6y=30 fromC0,-V5) to cra,O). X,

A: Line integral Given ellipse is  From .

Q: Which of these is the equation of an ellipse with a minor axis 6 units long and a major axis 14…

A: By using equation of ellipse formula, we find the required equation of ellipse

Q: Write the equation of the ellipse 16x? + 9y? – 64x + 90y + 145 = 0 in standard form (æ – h)? (y –…

A: We can make it easier for you

Q: What is the eccentricity of the ellipse whose equation is [(x2) / 25] +[(y-3)2 / 9] = 1?

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Q: Consider the equation of an ellipse written in terms of x and y as 13 z? + 8 yz + 7 y² = 1 a. Find…

A: Note:- For a non singular square matrix A,  A = PT D P  Here, P is orthogonal matrix that is, P-1 =…

Q: The graph of the equation a? + xy + y = 5 is an ellipse lying obliquely in the plane as illustrated…

A: Given equation of ellipse x2+xy+y2=5 Since you have posted a question with multiple sub-parts, we…

Q: 4. Find the equation of ellipse having its center at the origin, focus at (0, 3) and a vertex at…

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Q: Answer the following True or False: (x + 1)² Let (y + 8)? + + 8)? = 1 a2 62 be the equation of an…

A: SOLUTION: (x+1)^2/a^2+(y+8)^2/b^2=1 center=(-1, -8) but in question given center=(1,8) hence false

Q: Find an equation for the ellipse of eccentricity 2 /3 that has the line x = 2 as a directrix and the…

A: To determine the equation of the ellipse.

Q: Given an ellipse with the equation x²/36+y²+32=1, the distance between the foci is

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Q: Evaluate –dz , where C is the ellipse 4x² + 9y? = 1. %3D Yc z2 – 3z+2

A: Given: The equation: ∮C z3 + z + 1z2 - 3z +2dz Here C - ellipse of 4x2 + 9y2 = 1

Q: Given the ellipse 16x2 + 25y2 – 64x – 50y – 311 = 0, determine its center.

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Q: which of the following is a covertex of the ellipse 2 Sx2+ 1642-100x + ICoy-1100-0?

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Q: Graph the ellipse (x - 2)2/9 + (y - 1)2/4 = 1 and give the location of its foci.

A: Given equation of ellipse is (x-2)29+y-124=1

Q: Give the coordinates of the center, vertices, covertices and foci of the ellipse with the given…

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Q: Given an ellipse x2/a2 +y2/b2= 1, a  b, find the  equation of the set of all points from which there…

A: (Note: We are entitled to solve only one question at a time) Given: x2a2+y2b2=1, where a≠b. To Find:…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: