Prove that the circles x² + y2 + z2 - 2x + 3y + 4z - 5 = 0, 5y + 6z +1 = 0 x² + y2 + z2 - 3x - 4y + 5z - 6 = 0, x + 2y – 7z = 0 lie on the same sphere and find its equation.

Q: Find an equation of the sphere that passes through the origin and whose center is (4, 3, 4). X

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Q: Write the equation of a sphere that has a center at C(2, 5,-3) and contains points D(4, 1, 1) on the…

A: Given Data: The centre of the sphere is: C(h, j, l)=C(2, 5, -3) The point at the edge of the sphere…

Q: (a) Find the center and radius of the sphere defined by x² + y² +2²-8x + 2y + 8 = 0. (b) Find the…

A: A sphere is object that is 3-D analogue to a 2-D circle. If its center at the point (a, b, c) and…

Q: how that the point (1,0,-1) is the centre of the sphere passing through…

A: Let O=(1,0,-1), A=(1,8,-8) B=(-9,0,5) C=(7,-8,-1) D=(-7,0,7) It is enough to show that…

Q: Determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0

A: We have to determine the surface with the equation 2x2-3y2-4z2-12x-6y-21=0.

Q: Determine the coordinates of the center and the value of the ra sphere x2- y2-2- 10x - 6y - 12z --54…

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Q: What is the center of the sphere given by the equation x² − 6x + y² – 2y + z² + 8z + 17 = 0? -…

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Q: it) is the point (-1,-2,3) visible from the point (1.2, 0) if there is an opaque ball of radius 1…

A: With the help of two points  then we find x,y and z values .. Then we put x,y and z values in…

Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

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Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: If (a,B.y) is a point at which the surface x2+y2-z²-2x+12=0 has a horizontal tangent plane, then y|…

A: As per guidelines, we will solve first question only. Let α,β,γ be the point on the surface…

Q: The distance between the centers of the following two spheres: is x²-58x+y2+36y+z²=-1164,…

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Q: 7. Let z = -3 + 5i. Plot the points z,-z,7,-ž and - in the complex plane.

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Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: A circle with radius 2 contains the point (1,-4). Which of the following equations best describes…

A: The given point is 1, -4The radius is 2

Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: 5. Draw/Describe the set of points in the complex plane that satisfies |z - il < 2.

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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 x² + y² − 3x − 6y + 14 = 0, - equation of the circle which cuts th x² + y² − x − 4y + 8 = 0…

A: The circle having center at the radical center of the three given circles and radius equal to the…

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: 2) The diameter of a sphere has endpoints given by points P = equation of the sphere in standard…

A: The diameter of a sphere has endpoints given by points The Equation of sphere whose center and…

Q: 2) Find an equation of the plane that contains all points that are equidistant from the points…

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