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Equation in Sphere in Various Forms

Category : JEE Main & Advanced

(1) Equation of sphere with given centre and radius : The equation of a sphere with centre  \[(a,b,c)\] and radius R is \[{{(x-a)}^{2}}+{{(y-b)}^{2}}+{{(z-c)}^{2}}={{R}^{2}}\]                         ……(i)



If the centre is at the origin, then equation (i) takes the form \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}={{R}^{2}}\], which is known as the standard form of the equation of the sphere.



(2) Diameter form of the equation of a sphere : If \[({{x}_{1}},\,{{y}_{1}},\,{{z}_{1}})\] and \[({{x}_{2}},\,{{y}_{2}},{{z}_{2}})\] are the co-ordinates of the extremities of a diameter of a sphere, then its equation is \[(x-{{x}_{1}})(x-{{x}_{2}})+(y-{{y}_{1}})(y-{{y}_{2}})+(z-{{z}_{1}})(z-{{z}_{2}})=0\].

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