2) Consider two spheres (x - 2)² + (y - 3)² + z² = 1 x² + y² + z² = -8y + 2z + 3 a. What is the distance between the centers of the spheres? b. Find an equation of a plane that contains the centers of both spheres.

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

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Q: Find the distnace between the point and the plane. (2,8,4) 2x + y + z = 5

A: We know, The distance from (p,q,r) to the plane ax+by+cz+d=0 is  a.p+b.q+c.r+da2+b2+c2

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: 2. Consider the triangle with vertices at A = (0,0), B = (-6, –9), and C = (-15,0). (a) Find the…

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A: The answer provided below has been developed in a clear step by step manner

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Q: Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found…

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Q: Find the intercepts of the plane 4x+y+10z=40 . Write your answers as points (a,b,c) where a,b and c…

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Q: The following equation represents a sphere: x² + y² + z² = 1. Which one of the following is the…

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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: If the intersection points of the hyperbola 3x² – y² = 11 and the line 2x + y = 10 are P and Q,…

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

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Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

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