Find the area of the surface: the part of the Problem 2 paraboloid x = y² +2² that lies inside the cylinder z2 + y² = 9

Q: . Use the method of completing the square to write the following equation in standard form and…

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: A hyperboloid of two sheets Graph the surface defined by the equation - 16x? – 4y? + z? + 64x – 80 =…

A: Given: A hyperboloid of two sheets:  – 16 x 2 – 4 y  2 + z 2 + 64 x – 80 = 0.   To sketch: The graph…

Q: III. Consider the parabola C: z-4 = -(x - 2)² on the xz-plane. 3. Give an equation for the surface…

A: Given equation of parabola is:.The objective is to find an equation of the surface of revolution…

Q: The cylinder x² + y² = 25 intersects the plane x + z = 5 in an ellipse. Find the point on such an…

A: Given:The cylinder is: .The plane is .The cylinder intersects the plane in an ellipse.

Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

Q: Reduce the equation to one of the standard forms, classify the surface, and sketch it. (a) z23x²+4y²…

A: We have to reduce the equation in standard form, classify the surface and sketch the surface.Note:…

Q: What is the area of the ellipse x² 16 + y² 9 = 1?

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Q: What is the second coordinate of the center of the sphere of the equation below?…

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Q: Find the equation of the sphere with its center at (-2, 4, 13) and tangent to 3x + 4y - 12z = 10.…

A: Given: The center of the sphere is -2, 4, 13. To Find: The equation of the sphere with center -2, 4,…

Q: 2. Which equation represents a parabola with vertex (4,4) and directrix y = 2? Oy=2x² - 4x + 4…

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Q: Find the matrix A of the quadratic form associated with the equation. 3x2 2xy + 3y² + 8z² - 46 = 0 A…

A: The equation in the matrix form is Applying congruence operation on the matrix…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…

Q: The equation of the sphere with Center (4,-1,3) and radius √5 is

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Q: The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional…

A: Every surface equation with respect to an orthonormal coordinate system is written in a matrix form…