Find an equation of the largest sphere that passes through the point (-1, 1,4) and is such that each of the points (x, y, z) inside the sphere satisfies the condition x2 + y? + z? < 136 + 2(x + 2y + 3z)

Q: Determine an equation for the unique plane that passes through the points P(0,0, 2), Q(0,4, 0), and…

A: Given points are P(0,0,2), Q(0,4,0) and R(8,0,0). Find an equation for the unique plane that passes…

Q: Find an equation for the plane consisting of all points that are equidistant from the points  (−5,…

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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 center of the sphere whose one of its diameters has end points P1(1,-3,-1) and P2(2,0, 1) is…

A: Sphere Definition: A sphere is a three-dimensional counterpart of a circle, with all its points…

Q: a) Find the distance between the points (7,0,1) and (-5,4,2). b) Find the center and radius of the…

A: According to our guidelines we can answer only three subparts ,or first question and rest can be…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (-2, -2, 0)

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

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

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Q: Find an equation of the plane consisting of all points that are equidistant from (1, 0, -2) and (3,…

A: Let's assume the coordinates of all the points which are equidistant from a points (1,0,-2) and…

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

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Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

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Q: Find an equation of the plane consisting of all points that are equidistant from (0, -5, 2) and (-5,…

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Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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

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Q: Find an equation of the plane consisting of all points that are equidistant from (2, 4, 2) and (-2,…

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Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

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Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

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: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

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

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Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: Find an equation of the largest sphere contained in the cube determined by the planes x = 0, x = 8,…

A: given the planes:

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

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 point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: Find the points that are minimum to the origin and lie on the lines of intersection of planes: y +…

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Q: Find the equation of the sphere which passes through (2, 1, 3), (3, 2, 1), (1, –2, –3), (–1,1, 2).

A: Given that the sphere passes through the points (2,1,3), (3,2,1), (1,-2,-3), (-1,1,2).

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

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Q: A point moves such that the ratio of its distances from two fixed point is constant, show that its…

A: Let the moving point be P (x, y, z). Let A(a, 0, 0) and B(-a, 0, 0) be two fixed points.

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: Find an equation of the sphere concentric with the sphere x^2 + y^2 + z^2 + 4x + 2y − 6z + 10 = 0…

A: Topic = Geometry

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: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

A: Find an equation of the plane consisting of all points that are equidistant from (-2, -1, 0) and (0,…

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The center of the sphere whose one of its diameters has end points P;(1,3, –1) and P2(2,-2,1) is |…

A: Given that the endpoints of the diameter of the sphere are P11, 3, -1, P22, -2, 1 To find its…

Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

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Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O…

A: topic - shortest distance between point and sphere

Q: Find the equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25

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

Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

Q: Find an equation for the plane in R® spanned by the points (1,5, 1) and (1, 4, 2).

A: We have to find the plane equation for two given points

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: Find an equation of the plane through the three points given: P = (0,0, 2), Q = (-4, 1, –1), R = (2,…

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Q: Find the point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

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Q: Find the set of points that is satisfied the condition described by |z – 2i|+ |z + 4i| = 10

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Q: Find the points on the sphere x^2 + y^2 + z^2 = 1 that are closest to and farthest from the point…

A: Given sphere, x2+y2+z2=1 Consider gx,y,z=x2+y2+z2-1=0 The square of the distance between the points…

Q: Find an equation of the plane through the three points given: P=(0,0,3), Q=(2,−3,2), R=(−1,1,0)

A: find the equation of the plane

Q: find the equation of a sphere passing through the point(1,-3,4),(1,-5,2),(1,-3,0) and having on the…

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