Find a generating curve and the axis of revolution for the surface                             x2 + 3y2 + z2 = 9.

Q: Find the equation of the tangent plane to the surface z =9-(r² +y2) at the point (1,1,7). Write the…

A: Given surface is z=9-x2+y2⇒x2+y2 +z=9⇒x2+y2 +z-9=0 Take  fx, y, z= x2+y2 +z-9 And, Point say P is 1,…

Q: Consider the parabola C: z-4 = -(x - 2)² on the rz-plane. 1. Find the center-radius form of the…

A:

Q: 4d. z =-x´ + y´ Name of the surface

A: The structure obtained from the given equation is more like of dome structure

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Write the quadratic surface x2-y2+4z2+2x+4y+1=0 in standard form.

A:

Q: Consider the equation 4x² - 3y² + 12z² = -12. Describe the traces of this surface on the xy-plane,…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…

Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: Let S be the quadric with equation 36x2 –4y2 –9z2 – 36x = 0. Sketch a graph of the surface with…

A: See answer below.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.