# JEE Main & Advanced Mathematics Three Dimensional Geometry Condition of Tangency of a Plane to a Sphere

## Condition of Tangency of a Plane to a Sphere

Category : JEE Main & Advanced

A plane touches a given sphere if the perpendicular distance from the centre of the sphere to the plane is equal to the radius of the sphere. The plane $lx+my+nz=p$ touches the sphere ${{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2ux+2vy+2wz+d=0$, If ${{(ul+vm+wn-p)}^{2}}$= $({{l}^{2}}+{{m}^{2}}+{{n}^{2}})({{u}^{2}}+{{v}^{2}}+{{w}^{2}}-d)$.

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