x2 y2 4a2 a2 2a- ||

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: See the circular helix with equation D(t)= (-15 cost,15 sin t,8t). 1. Look for the value of t such…

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Q: Find the area of the surface generated by revolving the curve about each given anis. *- 7t. y= st,…

A: We have to find  the surface area generation by revolving the curve about x and y axis

Q: 42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the…

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Q: Find the arclength of y = 2a/2 on 1 <a< 2

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Q: Which of the following is simply connected? a) the horizontal strip Imz <1 b) the annulus 1</z <2 c)…

A: This is a problem of topology.

Q: 2 2 · ( \ )² + ( ² ) ²³ = = 1 in the first quadrant, find the following line integral with respect…

A: Given x62+y62=1 in the first quadrant  ∫C4x-5yds=

Q: Find the EXACT area inside the closed loop produced from the following parametric curve. Show ALL…

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Q: 3. Prove that the equation of the normal to the rectangular hyperbola xy = c² at the point P (ct,)…

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Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

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Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

A: Given: The parabolic cylinder lies over the triangle in the xy-plane with vertices (0,0),(0,4) and…

Q: Determine the roots of the indicial relationship for the Frobenius method applied to the following…

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Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

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Q: Find the arclength of y = 6x – 3 on 0 < x < 4. Give the exact answer. -

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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = ,…

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Q: See the circular helix with equation D(t)= (-15 cost,15 sin t,8t). 1. Look for the value of t such…

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Q: Work Problem1 a) Find the exact length of the curve 1 ,1< < 2. y = 4 3x b) Find the exact area of…

A: Given  curve  y=x34+13x    , 1≤x≤2

Q: 2 Find pxV 1+ 3x² dr, where P is the ellipse parametrized as follows: r(t) = , 0<t< 2n

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Q: QUESTION 4 The area bounded by the curves y = ²+1 and y =I+1 from intersection point to intersection…

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Q: The curve graphed below has the parametrization C = {(v 4 %3|

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

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 equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

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Q: Problem 5 For the shape given below, Determine the moment of inertia of the composite area about the…

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Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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Q: Consider the parametric equation  x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2).…

A: Given parametric equations - x = t2-1t2 = x+1t = x+1         .................(1)y =…

Q: 3. Evaluate (sin r +y cos r)dr + (sin r + z cos y)dy + sin ydz), where C'is the ellipse 36.r + 4y =…

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Q: Use Problem 6 to show that the area inside the ellipse x = a cos θ, y = b sin θ,0 ≤ θ ≤ 2π, is A =…

A: To show that the area inside the ellipse x=acosθ,y=bsinθ,0≤θ≤2π is A=πab. We know that…

Q: Question 11 Calculate the surface area of the given surface. The parabolic cylinder with equation z…

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Q: 1. Consider a fence whose base is the path with parametric equations |x(t) = cos³ t, |y(t) = sin³t,…

A: Given, A fence whose base is the path with parametric equations xt=cos3tyt=sin3t for 0≤t≤π2. Let the…

Q: Enter the appropriate value to answer the question or solve the problem. 6. Set up, but do not…

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Q: Solve the Laplace equation for a rectangular plate subject to the fol- lowing boundary conditions

A: Given: To solve the given Laplace equation for a rectangle plate subjected to the following boundary…

Q: The tangents to the rectangular hyperbola xy = c² and the parabola y = 4ax at their point of…

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Q: -7. х 3D sin?t, у— cos t yA

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Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: QUESTION 11 A three-dimensional solid obtained by revolving a region in the xy-plane about a line is…

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Q: Page 9 9. The curve y = x2 with 0Sx<1 is rotated about the y-axis. Find the exact area of the…

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Q: Problem 8: Determine the sphericity of cylindrical (h=5D) and disc (h =d/3) particles.

A: Formula of sphericity:

Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = ,…

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Q: Question 7 Evaluate the triple by using cylindrical coordinates. LL x²+y)dzdydx

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Q: 3) use to lce's Thuorem to calculate The cisculation The tield Px+ e'tzK around The curve c: The…

A: Stoke's Theorem: ∫CF.dr=∫∫S∇×F·ndS

Q: Question 5 of 5 Find the area of the surface of revolution generated by revolving the curve y = 3/a,…

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Q: Use the parametric equations of an ellipse, x = a cos(e), y = b sin(e), 0 se s 27, to find the area…

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Q: Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2).…

A: Consider the parametric equations  x = t2 − 1 and y = t2 + 2t

Q: Find the area of the region enclosed by the parametric equation x = t³ - 8t y = 4t²

A: This is a loop formed find graph  And then find limits of t

Q: Consider the ellipse + = 1. n/2 Show that the circumference of the ellipse is given by C 2 V4 cos? t…

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Q: x = 7 cos 0 y = 14 sin 0 0 <0< 2n

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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.