Write the ellipsoid 4.x2 + 16x + 3y? – 12y + 22 – 2z + 28 = 0 using spherical coordinates. Find the center and the half-axes of the ellipsoid.

Q: Find a parametric description for the ellipse 9x2+4y2+24y=0 oriented clockwise.

A: Ellipse

Q: Find the parametric equations for the ellipse y2 + 4x2 - 2y + 4x + 1 = 0. Hint: Use completing the…

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Q: Find the area of the surface formed by revolving the ellipse about the z-axis (an ellipsoid) y² + a²…

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Q: 7. The parametric equation of an ellipse is given by x = a cost, y=bsint; 0<t<2n. Determine the area…

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Q: Rotate the coordinate axes to remove the xy-term. Then name the conic section and sketch its graph.…

A: Given: x2+4xy-2y2-6=0 To Find: Rotate the coordinate axes to remove the xy-term.Then name the conic…

Q: The plane 15x + 20y + 40z = 195 intersects the cone z = x² + y² in an ellipse. The sum of the…

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Q: Match each equation with a description of the shape of its surface. 2 A. hyperbolic paraboloid B.…

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Q: The plane 6x + 8y+ 60z = 700 intersects the cone z? = r? + y? in an ellipse. The sum of the…

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Q: z' +z+1 Evaluate -dz , where C is the ellipse 4x + 9y = 1. c z² – 3z+2

A: By Cauchy integral theorem,            If the function fz in analytic in some simply connected…

Q: The plane 9x + 12y + 40z = 275 intersects the cone z? = x² + y? in an ellipse. The sum of the…

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Q: Find the required information and graph: , (x+3)² + (y – 1)² = 9 ssify the conic section: Center:…

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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: 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: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: 35. Calculate || 9x*+4y* dx dy, where D is the interior of the ellipse (G) + (4)' =

A: Given:

Q: 2 Write the equation of the hyperbola – 25 · x? + 16 · y² = 400 in standard form + = 1 %3D

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Q: Scalar line integrals Evaluate the following line integral along the curve C.

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Q: Consider the two ellipses in the x y plane given by the equations (x-1)2 2 =1 and (x+2)2 (y-5)2 62…

A: Given:  The given ellipse equations are x-1262+y232=1and x+2222+y-5242=1

Q: Decide which of the following equations may represent a circular conic section? Determine the…

A: The general equation of circle is : x-h2+y-k2=r2where centre =(h,k)             raduis =r

Q: Calculate ne4x+16y° dx dy, where D is the interior of the ellipse

A: Given,            ∫∫De64x2+16y2dxdy where D is the interior of the ellipse x42+y82≤1

Q: Find the equation of the conic in the rotated system that eliminates the cross-product term and find…

A: Given

Q: Identify and graph the conic whose equation is in attachment.

A: Consider the given equation as 5x2+4xy+2y2-285x-45y+4=0

Q: 4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this ellipse, find: 1. the ones…

A: 1. Note that the smallest and largest value of y occur when dy/dx =0. Taking derivative on both…

Q: Name the type of conic section defined by the following equation and give a parametrization of it:…

A: We know general equation of circle is given by  center at (a, b) of radius r is given by (x-a) ^2…

Q: 23 +z+1 Evaluate -dz , where C is the ellipse 4x + 9y² = 1. c z² – 3z +2

A: Consider ∫z3+z+1z2-3z+2dz Singularities of this function are the points at which denominator of the…

Q: Match the ellipsoids shown in the table with the equations. Answer Bank x2 + 2y2 + 2z² = 4 2x2 + 2y?…

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Q: The equation z? = 10 – x² – y? defines a/an %3D a) ellipsoid c) paraboloid b) cone d) hyperboloid

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Q: y2 - The ellipsoid 1 = 1 9 8. +

A: Vector-valued function: - A vector-valued operation incorporates a domain that's a set of real…

Q: 2. Which conic section is represented by the équation 2x2 + 4x- y +9 = 0? O Hyperbola Ellipse O…

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Q: F. dr, where C is the ellipse (x + 3)² + 5(y – 2)² = 16 and F(x, y, z) = x²i+ %3D Pj+ z°k.

A: Given: x+32+5y-22=16 Fx,y,z=x2+y2+z2

Q: Identify the conic sections below by completing the square on z and y to place them in standard…

A: The given equation is a) 4x2+3y2+8x-24y+40=0

Q: 4. Classify the following conics as a circle, parabola, ellipse or hyperbola and explain why. a) 9x?…

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Q: Find the extreme values of f(x, y) = e¬¤y for the points on the ellipse x² + 4y? = 1

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Q: For the quadric surface, - + z = = 1, setting the value of z = 1will give you which conic section? 4…

A: The given quadric surface is x24-y29+z=1  To find when z=1which conic section represents the…

Q: Find the equation of the surface of revolution generated by rotating the parabola y = z^2 around the…

A: A surface of revolution generated by rotating a curve described by y=f(z) around z-axis is given as…

Q: What is the conic given by the equation 5x? – 6xy + 5y? – 12 = 0? - O A. Real ellipse O B.…

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Q: Determine the length of the latus rectum and distance between the foci of the conic section: 16x^2…

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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 plane 9x + 12y + 40z = 275 intersects the cone z² = x2 + y2 in an ellipse. The sum of the…

A: We have to find the sum of the z coordinates of the highest and lowest points on the ellipse. This…

Q: Find the type of conic represented by the equation of the curve given by C=21 - 6xy+29y +6x-…

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Q: Consider the ellipsoid a? + y? + 4z2 = 12. 1. Find the general equation of the tangent plane to the…

A: We need to find the partial derivatives of the function w.r.t x,y,z for finding the equation of…

Q: The ellipse x^2/7^2 + y^2/6^2 = 1can be drawn with parametric equations where x(t) is written in the…

A: x272+y262=1since 7&gt;6 S0 major axis on x-axis

Q: Choose the equation that represents the graph of the cylindrical surface below O2 + y? = 1, = 5 O…

A: We have plotted the graph:- second option

Q: Find parametric equations for an object moving clockwise along the ellipse (x2/16)+(y2/9)=1…

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Q: In the conic section r2 36y, what is the distance between the focus and the center? %3D 0 6 O 12 O…

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Q: Find the focus, orientation and external conic x?_2ny +y?+2xbys3Q 1. center of the

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Q: . Find the cylindrical equation for the ellipsoid 4r² + 4y² + z² = 1.

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Q: The ellipse y? q? + = 1 x2 %3D a2 62 is rotated about the x-axis to form an ellipsoid. Find the…

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Q: Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0…

A: Given equation of the ellipse 9x2+4y2+24y=0.