Q9. Draw a sketch of a hypersphere in four dimensions.

Q: Draw the Taxi-metric hyperboloid |x| + |y| + |z| = 1

A: As per the question we are given the equation of Taxi-metric hyperboloid as : |x| + |y| + |z| = 1…

Q: Write the equation of Spheres with radius R.

A:

Q: The part of the hyperboloid 4x 2 - 4y2 - z2 =4 that lies in front of the yz-plane

A:

Q: Find a parametrization of the hyperboloid of two sheets (z2/c2) - (x2/a2) - (y2/b2) = 1.

A:

Q: Which of them are tr 1) Ellipsoid de + 16: Hyperbakid II) =D4- Sy-9 Perbled IV) Sphere

A: The equation of ellipsoid is of the form x2a2+y2b2+z2c2=1 So, (I) is true.

Q: Find the standard equation of the sphere with the given characteristics. endpoints of a diameter:…

A: Equation of the sphere

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given endpoints of diameter ::

Q: The surface z -- =1is a hyperboloid of two sheets. Select one: OTrue OFalse

A:

Q: 5. Find the equation for the sphere whose center is at (-1, 1/12-13) and radius is

A:

Q: Find an equation of the largest sphere with center (6, 2, 8) that is contained in the first octant.…

A:

Q: If AB is a double ordinate of the hyperbola *- y =1 such b? a* that AOAB (O is the origin) is an…

A: Introduction :

Q: Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel…

A: Given question:- Which degenerate conic section is formed when a double cone is sliced through the…

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Given that End points of diameter (2,9,13),(2,-7,-6)

Q: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

Q: 3. Where do the asymptotes intersect for the hyperbola y = ( 2x +3 ) / ( 8x +5 ) O ( 3/8 , 2/5 ) O…

A: Given : Hyperbola y =2x + 38x + 5   To find the asymptotes.

Q: Find the center and the radius of the sphere. x2+y2+z2+4x-5z=0

A: Comparing with standard equations of sphere,

Q: The surface z² = 1 is a hyperboloid of 36 25 one sheet. Select one: True False

A: The hyperboloid of one sheet given by the equation x2A2 + y2B2 - z2C2 = 1

Q: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A:

Q: Find the standard equation of the sphere with the given characteristics. Endpoints of a diameter:…

A: Solution: The objective is to find the standard equation of the sphere

Q: 4 1z = 4 –y? x = 4- 3 2 z + y = 2 z = y

A:

Q: Find the length of a,b,c of the given hyperbola: x^2/4 - y^2/5=1

A:

Q: The distance between the centers of the following two spheres: x²+10x+y²+14y+z²=-73,…

A: Given that: x2+10x+y2+14y+z2=-73      .......(1)2x2-4x+2y2+2z2+8z=-5     ........(2)

Q: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A: 2)circle

Q: 1-sketch the following hyperboloid z² – x² – y² = 1 %3D

A:

Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

A:

Q: The surface z - - = 1 is a hyperboloid of one sheet. Select one: True False

A: The general form of the equation of hyperboloid of one sheet is: x2a2+y2b2-z2c2=1

Q: Find the standard equation of the sphere with the given characteristics. endpoints of a diameter:…

A: Use standard equation of sphere

Q: A quadric surface, generally written in the form + += 1, is a hyperboloid if O at least one term in…

A:

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(-1,…

A: Equation of sphere  standard form of sphere equation

Q: A hyperbola is the set of points in a plane, the difference of whose distances from two fixed points…

A: Given : A hyperbola is the set of points in a plane the difference of whose distances from two fixed…

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: Find the radius and center of the sphere described by 3x2 + 3y2 + 3z2 + 6x – 6y = 3.

A:

Q: Calculate the curvature of the ellipse x2a2+y2b2=1 at its vertices.

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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: What is the shape of the vertical cross section of this solid figure that does not pass through the…

A: Topic:- cutting of surface

Q: Which of the following quadric surfaces most resembles a football or rugby ball? Select one: O a.…

A:

Q: Show that the maximum value of a2b2c2 on a sphere of radius r centered at the origin of a Cartesian…

A: Let fa,b,c=a2b2c2 subject to a2+b2+c2 =r2  The gradient equation is…

Q: Find the standard equation of the sphere with the given characteristics - Center: (3, −2, 6);…

A: We have to find the standard equation of the sphere where, center is given as 3, -2, 6 and radius is…

Q: Using the property of Re z and Im z to show that the hyperbola x2 - y? = 1 can be written as: z +…

A:

Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Find the equation of the surface of revolution generated by rotating the hyperbola x^2 - y ^2=1 ,…

A: \ Revolution of the hyperbola about its transverse axis generates a surface of two sheets, two…

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A:

Q: The quadric surface 2 = x² + is called

A: We know that this is the equation of hyperboloid from the general equation of hyperboloid.

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: A mirror for a reflecting telescope has the shape of a (finite) paraboloid of diameter 8 inches and…

A: It is given that, A mirror for a reflecting telescope has the shape of a (finite) paraboloid of…

Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: Find the dimensions of the rectangle of largest perimeter that can be inscribed in the ellipse x2/a2…

A: Let 2x,2y be the length and width of the ellipse that is inscribed in ellipse  Then , perimeter of…

Q: Find the standard equation of the sphere with the given characteristics Endpoints of a diameter: (0,…

A: Given: Endpoints of a diameter of sphere: a1, b1, c1 ≡(0, 0, 4) and a2, b2, c2 ≡(4, 6, 0)

Q: Find the equation of the sphere in standard form that satisfies the given conditions. diameter PQ,…

A: Distance between two points A(x1, y1, z1) and B(x2, y2, z2) is AB = x2-x12 + y2-y12 + z2-z12   The…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.