Find the standard equation of the sphere with the given characteristics. endpoints of a diameter: (0, 0, 8), (4, 6, 0)

Q: find the center and the radius of the circle  a)x^2 +(y+2)^2 =16   b) 2x^2+2y^2-4x+8y-14=0

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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: What is the center and radius of the circle? (x-2)2 +y? = 25 %3D The center of the circle is. (Type…

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Q: Find the coordinates of the center and the length of the radius of the given circle 3x2 + Зу? — 12х…

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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: 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 equation of a sphere if one of its diameters has endpoints (5, 4, 3) and (1, 6, -9)

A: Consider the endpoints of the diameter: (5, 4, 3) and (1, 6, -9) To calculate the diameter of the…

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

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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: ind the standard equation of the sphere  with diameter and end points below (6,-1,-2), (4,11,12)

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Q: Find the vertex, force, and directrix of the parabola x^2=7y

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Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] 3x2 + 3y2 +…

A: Given, equation is, 3x2+3y2+3z2+6x-6y=3.   The objective is to find the radius and center of sphere.…

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

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Q: Find the radius and center of the sphere. (Hint: Complete the square in each variable.] 3x2 + 3y? +…

A: topic - center and radius of sphere

Q: The area of the ellipse in the figure is three times the area of the circle. What is the length of…

A: Known facts: Area of ellipse is A=πab where a is length of semi-major axis and b is length of…

Q: Find an equation of a sphere if one of its diameters has endpoints (5, 0, 6) and (7, 4, 8).

A: Solution of the problem as follows

Q: Find the center and radius of the sphere with equation (x - 6) + (y + 6) + (z + 1) = 49 Center:…

A: The given sphere equation Compare with standard equation of the sphere To find out the centre and…

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

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Q: Using the given equation, identify the center and the measure of the radius, the graph in the sketch…

A: Compare this  x² + y² = 16  equation with (x - h)2+ (y - k)2 = r2 Where ( h , k) is the centre and r…

Q: A round trampoline is located in a rectangular back yard. The shape of the trampoline is modeled by…

A: (x+2)2+(y-3)2=49

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

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Q: Q1. Find the equation of sphere whose center is at (4,-1, 7) and radius is 5.

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

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Q: Find the standard equation of the sphere that has the point (-3, - 6, 0) and (3, 4, 5) as endpoints…

A: Given : The point (-3, -6, 0) and (3, 4, 5) as endpoints of a diameter of sphere.

Q: Determine the center-radius Form of the equation of the sphere whose diameter has endpoints at (2,…

A: The first question has been solved as per the request of the student.     The center radius form of…

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: For Exercise, write the standard form of the equation of the hyperbola subject to the given…

A: Given: Corners of the reference rectangle: (8, 7), (−6, 7), (8, −3), (−6, −3); Horizontal transverse…

Q: Find an equation of a sphere if one of its diameters has endpoints (7,9, 9) and (3, 5, 7).

A: Given end points of diameterA=7,9,9 & B3,5,7

Q: Find an equation of a sphere if one of its diameters has endpoints (7, 9, 9) and (3, 5, 7).

A: The endpoints of the sphere we have, (7,9,9) and (3,5,7)

Q: Find the equation of the sphere

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

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Q: Given the points A(3,1, 6), B(5, –1, –2), and C(1, –3, 2) a. Show that A, B, C form the vertices of…

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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: The equation of a circle is given below. Identify the center 53 2x-16x+2y+ 10y=-· 2

A: The equation of the circle is given by 2x2-16x+2y2+10y = -532 To evaluate : The center of the…

Q: find the center and the length of a radius of each circle. x2 + y2 - 16x + 6y + 71 = 0

A: given,

Q: Show that the equation represents a sphere, and find its center and radius. Please show all of your…

A: The general equation of a sphere is,

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: 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: For Exercise, write the standard form of an equation of a hyperbola subject to the given…

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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 centre and radius of the sphere determined by the equation x'+y* +(:-2)° =: 25

A: Given that sphere equation is - X2 + Y2 + (Z - 2)2 = 25 And we find radius and centre of the sphere.…

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: c) Find the center and radius of the sphere whose equation is x² + y? + z? + 10x + 4y + 2z - 19 = 0

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

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.