Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y +9z-108x-8y-72z+436 =0

Q: State the type of the quadratic surface: ()' - (5)' + (¿)° = 1 2 1. Ellipsoid 2. Hyperboloid of one…

A: Here we need to find the type of quadratic surface and it's trace obtained by the plane z=1

Q: Identify the type of surface represented by the equation z2 x2 %3D 10 10 6. Parabolic cylinder…

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Q: Identify the type of surface represented by the given equation. 를 - 2.2 2 8. O Parabolic cylinder…

A: The given equation is z22-x28=y2. As we know that the general equation of the parabolic cylinder is…

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: Find an equation for the surface obtained by rotating the parabola y=2 about the y-axis.

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Q: Consider the equation below. x² – y2 + z² – 4x – 2y – 4z + 7 = 0 - Reduce the equation to one of the…

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Q: State the type of the quadratic surface: (중)"- (1)" + (주)'=1 1. Ellipsoid 2. Hyperboloid of one…

A: NOTE: Refresh your page if you can't see any equations. . here two of the variables have positive…

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: Identify the quadric surface with equation -a + 9y? – z = 0. O elliptic paraboloid O hyperbolic…

A: given  -x2+9y2-z=0

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2…

A: We have to convert the given equation x2+y2=16 into spherical coordinates

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: 1. Find the area of the part of the surface z = a? + 2y that lies above the triangle with vertices…

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

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Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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Q: The plane 9x + 12y+ 40z = 275 intersects the cone z = coordinates of the highest and lowest points…

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Q: Identify the surface in the xyz coordinate system given by the equation: z=-√(4-y^2) O cylinder O…

A: Let's find.

Q: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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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: Identify and sketch the section of the surface at x = 0. 25.x + 16y² – 922 = 0 Type of the surface:…

A: For x=0, the equation becomes 16y2-9z2=0. And the graph looks like the following.

Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1. O elliptic…

A: To identify the surface that corresponds to given equation- 100y2-25x2-4z2=1.

Q: Sketch the curve of intersection of the surfaces. The ellipsoid 2x + 2y° + = 288 and the paraboloid…

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Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

A: Given z = 3-x2-y2 , above the plane z=-1

Q: For the surface 4x² + y² −z = 0, classify the indicated trace as an ellipse, hyperbola, or parabola.…

A: We have been given the equation  4x² + y² −z = 0           (1)

Q: Determine the projection of the following surface on the plane of the xy-axes -2y? + + =1 3 3 O…

A: -2y2+x23+z23=1To find the projection

Q: The portion of the surface z = 2x + y2 that is above the triangular region with vertices (0, 0), (0,…

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Q: Find a parametric representation for the lower half of the ellipsoid 5x² + 4y2 + z² = 1.

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Q: Put the quadric surface equation 4X (-8y + 4Z+39 = 0 into one of the standard forms, specify the…

A: The given quadric surface equation is           4x2+y2-z2-24x-8y+4z+39=0 Write the like terms…

Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: The plane x + y + 2z = 2 intersects the paraboloid z = x² + y² in an ellipse. What is the point on…

A: We will use Lagranges multiplier method to find optimal solution  To maximize/ minimize f(x,y,z)…

Q: State the type of the quadratic surface: ()* + () + 2? = 1 1. Hyperboloid of two sheets 2.…

A: Given equation represents surface  3. ellipsoid

Q: Find the equation of the surface of revolution that is generated by rotating the parabola y = x^2…

A: Equation of surface of revolution of a curve about y-axis is given by x2+z2=r2 where r is the radius…

Q: Does every second-degree equation in x, y, and z represent a quadric surface? Explain.

A: the equation of a quadric surface in space is a second degree equation in three variables. 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: Locate and classify the stationary points on the surface z=xy2-2xy-2x2-3x, remembering that  x, y ,…

A: Solving for stationary points of given function using partial derivatives

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

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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: Determine the projection of the following surface on the xz plane -y+ 름 =1 O Ellipse O Parabola O…

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Q: The part of the surface z =1  + 3x+ 2y 2 that lies above the triangle with vertices (0, 0), (0, 1)…

A: Part of the surface: z=1+3x+2y2∂z∂x=3, ∂z∂y=4yVertices of the triangles are (0,0) , (0,1) , (2,1)

Q: Identify and sketch the section of the surface at x = 0. 25x? + 16y² – 9z² = 0 Type of the surface:…

A: We need to sketch the section of the surface x=0, 25x2+16y2-9z2=0. For x=0, 16y2-9z2=0. The graph is…

Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

Q: Consider the ellipse given by the intersection of the plane x+y+7z=3 with the paraboloid x^2+y^2=2z.…

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Q: Identify the surface that corresponds to the equation 100y^2 - 25x^2- 4z^2 = 1.* O elliptic…

A: The various types of quadric surfaces are: the ellipsoid, the hyperbolic paraboloid, the elliptic…

Q: 11. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is? a. x² + y² + z²…

A: Equation of sphere is (x-h)2+(y-k)2+(z-l)2=r2. Where (h, k, l) is coordinates of the center.

Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: Identify the following surfaces as an elliptical paraboloid, hyperbolic paraboloid, a hyperboloid of…

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Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: Identify the surface by completing the squares. x + 4y? – 2 – 6x + 8y + 4z = 0 O An elliptic…

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Q: Identify the surface by completing the squares. x +16y² – z? – 14x + 32y + 8z = 0 O A hyperboloid of…

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