Find the point on the sphere x2+y2+z²=529 that is farthest from the point (-7,-11,-29).

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Which of the points A(9, 0, 3), B(6, 5, 6), and C(2, 9, 2) is closest to the yz-plane? Which point…

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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: Find the center and radius of the sphere. x2 +y2+z2 - 16x - 12y + 6z = -45

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Q: Determine the point on the plane 4x- 2y + : = 1 that is closest to the point (-2,-1,5)

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Q: Find the point on the sphere x2+y2+z2=1089 that is farthest from the point (-22,-17,-21).

A: Let, (x,y,z) be the point on the sphere g(x,y,z)=x2+y2+z2-1089=0...(1) which the maximum distance…

Q: Find the distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: Find the value of x and y in the rhombus. y° 3x 2x

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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: The equation of the sphere with center (2,-3, 10) that touches that y-axis is OA (x- 2)° + (y +3)* +…

A: Solution is given below:

Q: Find the equation for the plane through the points Po (0, – 4, – 5), Qo(4,2,3), and Ro (0,3, – 2).

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Q: The distance from the point S(7, 7, -6) to the plane 2x + 11y + 10z = 9

A: option C 2215 is correct detailed solution is given below

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 point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

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Q: Describe the set of points in 3-space defined by the equations x? + y² + z2 - 8z = 9, x = 3. %3D

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Q: Find the equation of the plane that passes through the points P1 = (2, 3, 1), P2 = (5, 4, 3), P3 =…

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

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Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find the point closest to the origin on the line of intersection of the planes y + 2z = 12 and x + y…

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Q: Find the point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200…

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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: 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 an equation of the sphere that passes through the origin and whose center is (-6, – 4, 12). OA.…

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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: Find the point on the sphere x^2 + y^2 + z^2 = 8 that is closest to the point P(2, 1, 1)

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Q: Determine the x coordinate of the point on the plane Π:−3x−2y+2z=2 closest to the point (2,5,−5).

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Q: Determine the center and radius of the sphere 2x2+2y2+2z2-12x-24y-36z=0

A: We have to find center and radius

Q: Find the radius and center of the sphere. x2 + y² +z² - 6x + 8y – 4z = - 13 r=

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Q: Identify and sketch the surfaces in space, 3-D. x² +y² = a² a) b) z = 4– x² – y² x² + y? - z? = 0 |

A: a)  x²+y² = a²

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: The surface 2x2 -2y² – 2z² =1 is identified as

A: The given surface is qudratic surface. Different qudratic surfaces 1)Ellipsoid 2)Hyperboloid in one…

Q: Find the equation of the plane that passes through the points P1 = (1, 1, 2), P2 = (2, 3, 3), P3 =…

A: The given points are:

Q: Find the equation for the plane through the points Po(1,5,5), Qo(- 1, – 5, – 5), and Ro (2,0, – 4).

A: NOTE: Refresh your page if you can't see any equations. . given points are

Q: The equation of the sphere with center (3,-10, 9) that touches that y-axis is OA. (r-3)2+ (y 10)+…

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Q: Find the center and radius of the sphere x2 + 18x + y? + 4y + z2 + 10z = –74 Center: ( || ) Radius:

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Q: What is the farthest point on the sphere x2 + y2 + z2 = 16 from the point (2

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Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

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Q: The point (6,-9, 7) is the center of the sphere represented by the equation x² + 12x + y² - 18y…

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Q: Find equations for the sphere whose center and radius is given in center(0,-7,0) radius 7

A: General equation of sphere is given by:

Q: Find the distance from the point A,= (-7,5, 8) to the plane – 5x + 4y+ 3z = -2. Enter the distance

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Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

Q: find the distance from the point to the plane. (2, 2, 3), 2x + y + 2z = 4

A: We have to find the distance from the point (2,2,3) to the plane 2x+y+2z=4

Q: Find the distance from the point (7,-9,-5) to the plane 3x + 5y = 51.

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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…