4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x%3=0, x+y%3D0 and x+y+z31, is x*+ya+z²-3(x-+y+2)=0.

Q: What are the vertices and foci of the hyperbola (x - 9)2/25 - (y + 6)2/144 = 1 Show all work.

A: We have to find the vertices and foci of the given hyperbola.

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

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

A:

Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

Q: The quadric surface, * - a - = 1 l is a hyperboloid %3D 64 None of these of one sheet that opens…

A: The given quadratic surface is: x24-y264-z216=1

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

A:

Q: Find the minimum and maximum squared distance between the sphere x² + y² + z² = 9 and the point…

A: We have to find the minimum and maximum squared distances between the sphere x2+y2+z2=9 and the…

Q: Write the sphere in standard form. 4x2 + 4y2 + 4z2 − 32x + 16y = 1

A:

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: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

A: The question is about Lagrange multipliers. Use the Lagrange multipler method to locate the point on…

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: close

A:

Q: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

A:

Q: Find the points on the surface xy2z3=2 that are closest to the origin.

A: Given, xy2z3=2We have to find the point on the given surface that are closest to origin.let the…

Q: Find the point on the sphere  x2+y2+z2=900 that is farthest from the point (−19,−8,11).

A:

Q: SET UP the necessary equations to find the point on the intersection of the surfaces x2 + 4y2 + 4z2…

A: The solution are next step

Q: Find the center and radius of the spherex2+y2+z2−6x−16y+ 20z=−92.

A: Topic - center and radius of sphere

Q: Find an equation of the largest sphere that passes through the point (-1, 1,4) and is such that each…

A: Find the equation of sphere.

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

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 center and the radius of the sphere. x2+y2+z2-3x-6z=0

A:

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Find the center and the radius of the sphere. x2+y2+z2+3x+3z=

A: See the details solution in below

Q: Find the equation of the sphere of radius at centered at (1, 4, 5)

A:

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

A:

Q: 2. What is the equation of a horizontal hyperbola with (x-4)² 81 (y + 3)² 81 (x-4)² 25 (x-3)² 25 (y…

A: Given problem:- What is the equation of a horizontal hyperbola with a center at (4,-3), a transverse…

Q: Determine the center of the sphere x2+y2+z2+8x+6y+10z=0.

A:

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: The equation of the sphere with center (9,-6, 10) that touches that -axis is OA (x - 9)? + (y +6)* +…

A: The general equation of the sphere with center (a, b, c) is given by (x-a)2 + (y-b)2 + (z-c)2 = r2…

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

A:

Q: Find the point on the sphere x²+y2+z²=1225 that is farthest from the point (6,9,24).

A:

Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

A:

Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

Q: 6. Find an equation of the sphere that passes through the origin and whose center is (3, 1, 3).

A:

Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

A: Let (x ,y, z) any point on surface. We have to minimize function f(x,y,z) = x2 + y2 + z2 under…

Q: 9. Find the center and radius of the sphere given by 3x + 3y? + 3z2 = 10 + 6y + 12z.

A:

Q: The equation of the sphere with center (7,-10, 1) that touches that y-axis is

A: To find the equation of the sphere we need center of the sphere  radius of the sphere.  Here given…

Q: 4x? + у? - 327 25 3z2 = 25

A:

Q: Find the point on the sphere X+y+=4 and the point on The sphere x+y ansi- 2 Selution:-

A: To find the point on the sphere which is farthest from the given  point (1,-1,1).

Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

A: The quadric with equation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10 where a is a parameter. We need to…

Q: The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

A:

Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: The vertices of hyperbola: 9z? – 4y² = 36, will be Select one: O (0, ±3) O (12,0) O (+3,0) O (0, ±2)

A:

Q: Identify the quadric surface as an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets,…

A: Here is the solution of the given problem.

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

A: