This exercise refers to the ellipsoid 36x + 4y² + 72z² = 288. Find an equation of the elliptical trace in the plane z = V2. 36 y? 1 12 O y? 1 8. 36 1 4 II + + + + +

Q: This exercise refers to the hyperbolic paraboloid z = y – 3x2. Find an equation of the parabolic…

A: Solution is given below:

Q: This exercise refers to the ellipsoid 4x² + 49y² + 28z² = 392. Vĩ. Find an equation of the…

A: Let's find.

Q: Write the ellipsoid 4.x2 + 16x + 3y? – 12y + 22 – 2z + 28 = 0 using spherical coordinates. Find the…

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Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: 1. Consider the ellipsoid x² + y² + 4z? = 12. (a) Find an equation of the tangent plane to the…

A: As per bartleby guideline for more than one question, only 1st one is to be answered. Please upload…

Q: Calculate | [(a4 – 3y) da + (2y³ + 4.x) dy] wherein r(t) = (3cos(t), 3sin(t)), 0 <t < 27, is an…

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Q: Choose the equation that represents the graph of the cylindrical surface below O a² + z² = 1, y = 5…

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Q: Show that the ellipse x = a cos t, y = b sin t, a 7 b 7 0, has its largest curvature on its major…

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Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: Let C be the boundaries of the ellipse 49x2 + 9y? = 49 taken in the counterclockwise direction. A…

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Q: Find an equation of the plane that contains the intersection points of the ellipsoid 9x? + 4y² + 9z²…

A: GIVEN : Ellipsoid 9x2 +4y2 + 9z2 = 36

Q: 5. Use the equation x2 = 4y² + 16z², to answer the following questions: %3D (a) What is the trace in…

A: (Note: We are entitled to solve only one question at a time and upto 3 subparts only) Given:…

Q: Consider the ellipsoid 4x? + y?+ 222 = 25. Find all the points where the tangent plane to this…

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0&lt;=…

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Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

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Q: z = 9x? + 9y? O b. z= 3x2 + 3y? O c. z= 4x? + 4y? O d. z= x2 + y? z = (x – 3)2 + y² Oc. O e.

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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: This exercise refers to the hyperbolic paraboloid z = y – 6x². Find an equation of the parabolic…

A: Given:- z = y2 - 6x2 To find:- Equation of parabolic trace in plane x= 3

Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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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: When the plane x = 3 passes through the surface x2 + y? + z² = 64, %3D the curve that forms from…

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Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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Q: Let C be the portion of the ellipse 4x² + (z – 1)² = 16 on the xz-plane with endpoints at (2,0, 1)…

A: Given : C is the portion of the ellipse 4x2+z-12=16 on the xz-plane with endpoints at 2, 0, 1 and 0,…

Q: (b) Find a parameterization, in spherical coordiantes, for the ellipsoid 4x2 + 9y2 + 2²/4 = 1 that…

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Q: (b) f(x, y) dA where D lies below the paraboloid z = x2 + y?, above the ry-plane, and inside the %3D…

A: Let's find.

Q: 1. (a) Parametrize the curve of intersection of the sphere a? + y? + 22 22 + 222 = 1, Try your best…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: For which point y on the ellipsoid æ² + 2y² + 4z² =1 (shown below) is %3D the quantity x+ y+ z as…

A: Lagrange's Multiplier:- To find:- Extreme values of f(x, y, z)…

Q: Write an equation of the tangent plane to the ellipsoid (a – 5)? + 4y? + 222 : М(5, 3, 1). = 38 at…

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Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Determine the intersection of the hyperbolic paraboloid z = (y2/b2) − (x2/a2) with the plane bx + ay…

A: Given The hyperbolic paraboloid equation is z=y2b2-x2a2 and the plane bx + ay − z = 0 .

Q: For the surface x? + y? = 2z? a) Find an equation in cylindrical coordinates

A: In this question, the concept of conversion of the coordinate system is applied. Cartesian…

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

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Q: Find the point on the ellipsoid x2 + y2/4 + z2/9 = 1 for which x + y + z is largest.

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Q: Calculate | [(a* – 3y) dæ + (2y³ + 4x) dy] wherein y(t) = (3cos(t), 3sin(t)), 0 <t < 2ñ, is an…

A: Please check step 2 for the solution.!

Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: (a) Write down an equation for the tangent plane to the ellipsoid 2a2 + 3y? + z? = 25 at the point…

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Q: The surface z? = x² + y? – 4x + 5 remains unchanged when rotated about the line L in R Which of the…

A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…

Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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Q: Which of them are true? I) 1 Ellipsoid 4 II) y? = 4x² + 16z² Hyperboloid III) x = 4 – 5y? – 9z?…

A: To find the correct choice from the following quadric surfaces.

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: Which of the following is that orientation of the ellipsoid 3x + y? + 2z2 =1 %3D where the outside…

A: The given problem is to find the positive orientation of the given ellipsoid. Given ellipsoid…

Q: The surface area of the cap cut from the paraboloid y + z? = 3x by the plane x = 2 is Select one or…

A: Given the paraboloid  y2+z2=3x  we have to find the surface area of the cap cut from the paraboloid…

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

Q: 1F M is the centroid of BC, AM= 44, CE= 54, and DM =23, find each missing measure.

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Q: Find a vector parametric equation for the ellipse that lies on the plane z (x + 2 - cylinder x + y =…

A: Dear student. You have posted many parts, according to the policy we will answering the first part.…

Q: Find the cylindrical equation for the ellipsoid 4x2 + 4y² + 2² = 1.

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Q: Find the point at which the line with parametric equations x = 3 + 4t, y = 5 – 2t, z = 4 + 7t…

A: According to question,Given equation of line in parametric form,x = 3+4t,y = 5-2t,z= 4 +7t,Equation…

Q: Show that the projection into the xy-plane of the curve of intersection of the parabolic cylinder…

A: To show : the projection into the xy-plane of the curve of intersection of the parabolic cylinder…

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.