QUESTION 10.3
Writing the Equation of a Sphere Given its Center and Radius Choose one $\cdot 5$ points
Write the equation of a sphere with center $\vec{c} = (2, 1, - 5)$ and radius $R = 3$
$(x - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 9$
$(z - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 3$
$(x + 2)^{2} + (y + 1)^{2} + (z - 5)^{2} = 9$

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Final Answer: $(x - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 9$

Steps

Step 1 ：The equation of a sphere in 3D space is given by the formula: $(x - h)^{2} + (y - k)^{2} + (z - l)^{2} = r^{2}$ where (h, k, l) are the coordinates of the center of the sphere and r is the radius of the sphere.

Step 2 ：In this case, the center of the sphere is given as (2, 1, -5) and the radius is given as 3.

Step 3 ：Therefore, the equation of the sphere should be: $(x - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 3^{2}$

Step 4 ：The equation of the sphere is correctly calculated as $(x - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 9$ . This matches the first option provided in the question.

Step 5 ：Final Answer: $(x - 2)^{2} + (y - 1)^{2} + (z + 5)^{2} = 9$

QUESTION 10.3Writing the Equation of a Sphere Given its Center and Radius Choose one ⋅5 pointsWrite the equation of a sphere with center c→=(2,1,−5) and radius R=3(x−2)2+(y−1)2+(z+5)2=9(z−2)2+(y−1)2+(z+5)2=3(x+2)2+(y+1)2+(z−5)2=9

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