12.2: Problem 3 Previous Problem Problem List Next Problem (1 point) Find the eq

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12.2: Problem 3 Previous Problem Problem List Next Problem (1 point) Find the equation of the sphere centered at (6,9,-3) with radius 9. Normalize your equations so that the cofficient of x2 is 1. 0 Give an equation which describes the intersection of this sphere with the plane z =-2. 0 Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 18 times. Your overall recorded score is 50%. You have unlimited attempts remaining. Email instructor

Explanation / Answer

1)

if (a,b,c) is center and r is radius, general equation of sphere is

(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2

Here:

a = 6, b=9, c = -3 and r = 9

So the equation is:

(x-6)^2 + (y-9)^2 + (z+3)^2 = 9^2

x^2 - 12x + 36 + y^2 - 18y + 81 + z^2 + 6z + 9 = 81

x^2 + y^2 + z^2 - 12x - 18y + 6z + 129 = 81

x^2 + y^2 + z^2 - 12x - 18y + 6z + 48 = 0

This is 1st answer

2)

z=-2 intersect it

so, we will put z=-2

x^2 + y^2 + (-2)^2 - 12x - 18y + 6(-2) + 48 = 0

x^2 + y^2 + 4 - 12x - 18y -12 + 48 = 0

x^2 + y^2 - 12x - 18y + 40 = 0

This is 2nd answer

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