Show that the given equation represents a sphere and find its center and radius x² + y2 + z? + ax + by + cz + d = 0 Where a² + b² + c² > 4d

Q: find the center and the radius of the sphere x^2+y^2+z^2+2x-5z=0

A: Equation of the sphere is  (x-a)² + ( y-b)2+ (z-c)2 = r2  Where (a,b,c) are the centre and r be the…

Q: Find the standard equation of the sphere with center C and rad C(1, v2, -5); r= 3

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Q: find the center and radius of the sphere x^2+y^2+z^2+8x-8y+6z=-16

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Q: (a) Identify and graph the quadric surface -r - y + 2? = 1.

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Q: a) Find the center of the sphere satisfying the equation, x2 + y2 + z2 - 2x + 4y + 2z = 10.…

A: The given equation of sphere,   x2+y2+z2-2x+4y+2z=10

Q: Find the center and radius of the sphere x? - 10x – 10 +y? + 14y + z² – &z = 0 O A C (5,7, -4), r =…

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Q: 28. The equation of a sphere with center (a, b. c) and radius r is (x- a) + (y – b)? + (; – c)? =…

A: Given,   The equation of a sphere is given  x-a2+y-b2+z-c2=r2  To justify it with the distance…

Q: Find the standard equation of the sphere. (Let  r = 9 and C = (3, 8, 9).)

A: equation of sphere where center ( a, b ,c ) radius r

Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

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Q: Write the equation of the sphere in standard form. + y? + z? + 12x - 8y + 2z + 44 = 0 Find its…

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Q: Consider the following equations of quadric surfaces: z =+-4 y? b) 4x² + (2) - - 2z? = -1 %3D | 16

A: The quadratic surfaces are given below-

Q: Find the equations of planes that just touch the sphere (x – 5)? + (y – 5)² + (z – 2)² = 4 and are…

A: We have given the equation This is a sphere of radius 2, and with a center at (5, 5, 2).

Q: Which of the following is the equation of a sphere with radius r = (-1,0,-2)? Select one: O None of…

A: This question is related to equation of sphere, we will solve it using given information.

Q: close

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Q: Which of the following point is the closest point on the sphere a? + y? + z? = 4 from the point…

A: Given: The given sphere is x2+y2+z2=4 and the point is (3,1,-1)

Q: Find the center and radius of each sphere. Sphere: x? + y? + z² – 10x - 8y + 6z = 0 Center: Radius:…

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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: b. z= 4x2 + 4y²

A: The equation describes surface of elliptic paroboloid.

Q: Find the center and radius of the sphere: x^2+y^2+z^2-8x+2y+4z-9=0

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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Q: Answer the following questions about the sphere whose equation is given by 1 + y + 2 - 6r + 4y = 36|…

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Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

A: Given, x2+y2+z2=1   ;   point (2,1,2)

Q: Answer the following questions about the sphere whose equation is given by 2+7 +2 - 8z + 6y = 75. 1.…

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Q: Find the center and radius of the following sphere: x2 + 2x + y? + z2 + 4z + 1 = 5

A: The equation of the sphere is x2+2x+y2+z2+4z+1=5 To find its center and radius.

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 11, – 2).…

A: Given: Origin point : ( 0 , 0 , 0 ) Center : ( -10 , 11 , -2 )

Q: Show that the equation represents a sphere, and find its center and radius: x^2+y^2+ z^2-8x + 6y +…

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Q: Find the standard equation of the sphere. (Let r = 5 and C = (9, 7, 5).)

A: Standard equation of a sphere with radius r and centre at c=(h,k,l) is  (x-h)2+(y-k)2+(z-l)2=r2

Q: (b) Find the points where the line passing through (-2,0,1) and (-4,1,4) intersect the sphere x2 +…

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Q: Answer the following questions about the sphere whose equation is given by 2² + y? + 2? – 6z + 4y =…

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Q: Find the shortest and longest distance from the point (1,2, -1) to the sphere x2 + y? + z? = 24 %3D

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Q: Write the equation of the sphere in standard form. x2 + y2 + z? + 6x – 2y – 2z = 14 Find its center…

A: Consider the equation of a sphere : where a,b,c are coordinates of the center of circle from the…

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: Try to visualize the set of all points (x, y, z)in a coordinate space that are twice as far from the…

A: a) Suppose the distance between two points  A(x, y, z)  and the origin   Plug into the distance…

Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: The sphere, x + y² + z? – 4y + 2z – 20 = 0, has a center at which point? (0,-2,-1) (0,2,-1) (2,1,1)…

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Q: Find the standard equation of a sphere that has diameter with the end points given below. (3, 8,…

A: to find standard equation of sphere that has diameter with end points 3,8,-2,-1,4,10

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: Which of the following represents the radius of the sphere whose equation is x² + 8x +y2 – 16y +z² –…

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Q: Find the center and radius of the sphere x? - 16x – 7+y? + 10y + z² – 4z = 0 OA C(8,- 5,2), r = 10 O…

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Q: Find an equation for the sphere centered at (1, -2, 3) containing the origin. V14 = x + y+ z 14 = x?…

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Q: Find an equation of the sphere containing all surface points P = (x, y, z)  such that the distance…

A: Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance…

Q: Write the sphere in standard form. x + y + z? 6x + 2y – 2z = 14

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

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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 center and radius of the sphere x2 – 12x – 4 +y? + 4y + z? – 20z = 0 ОА С (6, - 2,10), r…

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Q: find the equation of a sphere. x^2 +y^2 + z^2 +2x - 2z -2 = 0

A: see the details solution in below

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

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Q: Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (1) What is the equation of the sphere…

A: Answer

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.