Find the centre and radius of the sphere passing through the points O(

1.	Find the centre and radius of the sphere passing through the points O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c).
Answer» Let H(x, y, z) be the centre of the sphere so that HO = HA = HB = HC = Radius. Now HO = HA = (x - a)²+ y²+ z² = x² + y² + z² x = a/2 Similarly HO = HB y = b/ 2 and HO = HC z = c/ 2 Therefore, the centre H is given by (a/2, b/2, c/2) and the radius is given by HO = 1/2 √(a² + b² + c²)

Find the centre and radius of the sphere passing through the points O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c).

Answer»

Let H(x, y, z) be the centre of the sphere

so that HO = HA = HB = HC = Radius. Now

HO = HA

= (x - a)²+ y²+ z²

= x² + y² + z²

x = a/2

Similarly

HO = HB

y = b/ 2

and HO = HC

z = c/ 2

Therefore, the centre H is given by

(a/2, b/2, c/2)

and the radius is given by

HO = 1/2 √(a² + b² + c²)

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Find the centre and radius of the sphere passing through the points O(0, 0, 0), A(a, 0, 0), B(0, b, 0) and C(0, 0, c).

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