Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Show that the equation represents a sphere, and find its center and radius: x? + y? + z2 – 2x – 4y +…

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Q: Find the center and radius of the sphere x? + y? + z? - 6y + 8z = 0 Find an equation of the sphere…

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

Q: Find the center and radius of a sphere with the equation: 8x + 4z = 1 − 2x^2 + 20y − 2y^2 − 2z^2.

A: Given the equation of the sphere 8x+4z=1-2x2+20y-2y2-2z2

Q: Find the center and radius of the sphere x + y + z² +4x+6y-10z+2=0 and graph the sphere.

A: x2+y2+z2+4x+6y-10z+2=0 We need to find the center and radius of the given sphere and graph the…

Q: 5. Show that the equation represents a sphere, and find its center and radius: x²+y? + z2 – 8x – 10y…

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Q: Find the center and the radius of the sphere x + y² += - 4x+ y-6z+13=0 Center: Radius:

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Q: 1. Find the center and radius of the given equation of the sphere. x + y +z´ - 4x+ 6z+12=0

A: Given: The equation of sphere is x2+y2+z2-4x+6z+12=0.

Q: nd an equation of a sphere if one of its diameters has endpoints (54.

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Q: (a) , Find an equation of the sphere that passes through the point (-3,2,-1) and centered at the…

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Q: Complete the square to write the equation of the sphere in standard form. Find the center and…

A: On simplification, we get

Q: Complete the square to write the following equation as standard equation of a sphere and find center…

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Q: Find the center and the radius of the sphere. x2 +y? +z? +5x + 6z = 0

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Q: Find an equation of the sphere whose endpoints of a diameter are (-2,0, 5) and (-1,2, 3).

A: To find the length of the diameter use the distance equation Therefore, D=-2-(-1)2+0-22+5-32…

Q: Write the equation of the sphere in standard form. 9x? + 9y? + 9z2 = 36x – 12y – 24

A: The givne equation of the sphere is 9x2+9y2+9z2=36x-12y-24

Q: Complete the square to write the equation of the sphere in standard form. Find the center and…

A: Equation of sphere with Centre (a,b,c) and Radius 'r' can be written as: x-a2+(y-b)2+(z-c)2=r2 Using…

Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

Q: . 2x2 +2y? + 2z2 = 8x- 24z +1

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Q: c) Find the center and radius of the sphere whose equation is

A: Given, we need to evaluate the norm of the following vectors. i=<-1,2,4>ii=-i+7j

Q: Find the center and radius of the sphere with equation (x + 1)² + (y + 2)² + (z – 2)² = 4 Center:…

A: Explanation of the solution is given below...

Q: Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3).

A: I have appended the formula used in the solution part.

Q: a) [. Show that the equation 6x + 6y6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find an equation of the sphere whose endpoints of a diameter are (-2, 0, 5) and (-1, 2, 3).

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Q: 16. 3x² + 3y? + 3z² = 10 + 6y + 12z

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

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Q: Complete the square to write the equation of the sphere in standard form. Find the center and…

A: 9x2 + 9y2 + 9z2 − 6x + 18y + 1 = 0

Q: Show that the equation represents a sphere, and find its center and radius: x²+y² + z² – 8x + 6y +…

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Q: x² +y? + z² + 8x – y + 5z = 2

A: solution

Q: Find the center and radius of the sphere with equation (x + 2)2 + (y - 3)2 + (z + 6)² = 16 Center:…

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Q: a) [ Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find its…

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Q: Find an equation for the sphere with a) center at the origin and radius length r = b) center (2, –…

A: Let the coordinates of centre of sphere be a, b, c and radius be r.

Q: Find the equations for the spheres whose center is (7, -1, 5) and radius is 2.

A: To find: The equation of sphere whose centre and radius given. Given: The centre of sphere is 7,-1,5…

Q: Find the center and radius of the sphere (3x^2)+(3y^2)+(3z^2)-(6y)-(12z)-10=0

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Q: For the sphere with equation (x - 1) + (y + 2) + (z + 4) = 36, find a) the center. b) the length of…

A: The given sphere equation is x-12+y+22+z+42=36.

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: Find the radius and centre of the sphere x + y + – 4x + 2y-6z-11=0.

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Q: What is the second coordinate of the center of the sphere of the equation below?…

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

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Q: Find the centre and radius of the sphere determined by the equation x' +y° +(z - 2) = 16 %3D

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Q: find the standard equation of the sphere with center (4,3,3) and radius 7

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Q: a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = -20 represents a sphere, and find…

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Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 3, – 2). O…

A: We know that,  General equation of sphere is given by, (x-a)²+(y-b)²+(z-c)²= R² where, R is the…

Q: Find the center and radius of the sphere with equation (x + 3)² + (y + 1)² + (z − 1)² = 64 Center:…

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Q: Write the sphere equation x^2 + y^2 + z^2 + 2x - 2y -2z = 33 in standard form, and hence find the…

A: x2 + y2 + z2 + 2x -2y - 2z = 33To Find: The center and the radius of the sphere.

Q: Find the center and radius of the sphere with equation (z + 3)² + (y + 1)² + (z+4)² = 1 Center:…

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Q: Describe and sketch the graph of the given equation in R³, If it is a sphere, find its center and…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: Complete the square to write the equation of the sphere in standard form. x² + y² + z? + 9x - 2y +…

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Q: The equation x +4y² = 4 in three-dimensional space is an equation of which surface? O Ellipse O…

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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…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.