Find the radius and center of the sphere. (Hint: Complete the square in each variable.] 3x2 + 3y? + 3z? -42x +42y = 3

Q: (b) Find the equation of the sphere in R³ that has the diameter from A(1, 2, -1) to B(5,-2,0).

A: Part (b):- Given co-ordinates of diameter are  A1, 2, -1   to   B5, -2,  0.

Q: Q2 a) { ] Show that the equation 4x - 8y + 12z + 2x² + 2y² + 2z² = −20 represents a sphere, and find…

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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: ²+y? + - 2x – 4y + 8z + 17

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Q: Q.1/ a- Find the radius and center of the equation 9x2 + 9y² - 6x - 107 = 36y %3D

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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: O. Determine the vertex of the parabola y = x? – 14 + 40 by completing the square.

A: The parabola is  y = x2 -14x + 40

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: Find the centre and radius of the sphere determined by the equation x² + y? +(: -1 = 4

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

A:

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

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

A:

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

A: The given equation of sphere is: x2+y2+z2+9x-2y+10z+23=0

Q: x + y? + &x- 6y – 15 = 0

A: Complete the square to determine if the equation is a circle, quadratic (parabola) or other. Show…

Q: Complete the square to find the center and radius: x^2+y^^2+8x+8y=0

A:

Q: 5. Show that the equation represents a sphere, and find its center and radius:…

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Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

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

A:

Q: Use the completing the square procedure to rewrite the given equation in a center-radius form and…

A:

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: Find the center and radius of the sphere with equation (r – 1)? + (y + 4)² + (z+ 6)² = 16 %3D…

A:

Q: 9. The equation of the hyperbola is of the form (x – h)? (y - k)² (a) a? (y – k)? (x - h)² (b) a? (x…

A: Answer: (a) (a)(x-h)2a2-(y-k)2b2=1(b)(y-k)2a2-(x-h)2b2=1

Q: Write the equation for a sphere centered at the point (6, 1, - 3) and has the point (10, - 2, -8).

A:

Q: The three-dimensional quadric figure below is described by: x² + 2y? + 2z – 5 = 0

A:

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 5x - 2y +…

A:

Q: Find the center and radius of the sphere with equation (æ + 4)? + (y – 4)² + (z + 3)? = 49 Center:…

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Q: Find the radius and center of the sphere. [Hint: Complete the square in each variable.] x? + y? +z?…

A: We will find the centre and radius of sphere as shown below

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

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Q: 5. The equation x² + y? + 2 y +z2 - 2 z = 0 is a sphere. Determine its center and radius.

A: Follow next step

Q: III. Transform the equation of the parabola to the standard vertex for: completing the square. 16.…

A: Since we are given with multiple number of question and our guideline is solve first question only…

Q: Find the equation of the sphere

A:

Q: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 9x - 2y +…

A:

Q: Find the point on the ellipse x? + 4y? + 2xy = 12 with the greatest x-coordinate. (Use decimal…

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

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

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Q: 10. Complete the completing the square method on the equation below to find the center and radius of…

A: To find the center and radius of the circle.

Q: Find the coordinates & radius of the circle by completing the square. Equation of circle P: x2 + y2…

A: We have to find centre and radius

Q: A surface in space is defined by the equation x2 – y? + z2 + 5 = 0. Which one of these is true? The…

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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: Farmer Jones, and his wife, Dr. Jones, both mathematicians, decide to build a fence in their field…

A: We have to find the area of the enclosed region.

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: Complete the square to write the equation of the sphere in standard form. x2 + y2 + z2 + 5x - 2y +…

A: Given

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 +…

A:

Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: Let's practice on how to complete the square because this will help us to identify whether the given…

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