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Question

# Find the equation of a sphere, whose centre is (1,1,1) and radius is 5 units

A

x2+y2+z2xyz=5

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B

x2+y2+z2xx2y2z=5

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C

x2+y2+z2xyz=25

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D

x2+y2+z22x2y2z=22

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Solution

## The correct option is D x2+y2+z2−2x−2y−2z=22 Sphere can be thought of as a three dimensional extension of a circle. Similar to distance formula and section formula, the equation of sphere has additional terms involving z coordinate. To find the equation of the sphere, let’s consider a general point P(x,y,z) on the sphere. Let the centre of the sphere be O(1,1,1). We are given that the radius is 5 units. Distance of P from O will be equal to the radius, that is 5 units. Using distance formula, we get PO=√(x−1)2+(y−1)2+(z−1)2=5⇒(x−1)2+(y−1)2+(z−1)2=25⇒x2+y2+z2−2x−2y−2z=22 This is the equation of the sphere with centre (1,1,1) and radius 5 units

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