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lions [1.4K]
2 years ago
12

Find an equation of the sphere that passes through the point (6, -2, 3) and has center (-1, 2, 1). Find the curve in which the s

phere intersects the yz-plane. Find the center and radius of the sphere
X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0
Mathematics
1 answer:
svet-max [94.6K]2 years ago
5 0

Answer:

A)  x^2 + 2x+ y^2 - 4y + z^2 - 2z - 63 = 0

B) radius = 5

center  = (4,-1,-3)

Step-by-step explanation:

x^2 + y^2 + z^2 - 8x + 2y + 6z + 1 = 0

A ) Determine the curve in which the sphere intersects the yz-plane

determine the radius ( r ) =  √((6-(-1))2+(-2-2)2+(3-1)2) = √69

next the equation of the sphere ( curve in which the sphere intersects the yz-plane )

x^2+2x+y^2-4y+z^2-2z-63 = 0

B) determine the center and radius of the sphere

X^2 + y^2 + z^2 -8x + 2y +6z + 1 = 0

(x-4)2+(y+1)2+(z+3)2 = 25 = 52

radius = 5

center  = (4,-1,-3)

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