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 \[{{(ul+vm+wn-p)}^{2}}\]= \[({{l}^{2}}+{{m}^{2}}+{{n}^{2}})({{u}^{2}}+{{v}^{2}}+{{w}^{2}}-d)\].

Intersection of Straight Line and a Sphere

Other Topics

Co-ordinates of a Point in Space
Distance Formula
Section Formula
Triangle and Tetrahedron
Direction Cosines and Direction Ratios
Projection
Angle Between Two Lines
Straight Line in Space
Changing Unsymmetrical form to Symmetrical Form
Intersection of Two Lines
Foot of Perpendicular from a Point to The Line
Shortest Distance Between two Straight Lines
Definition of Plane and Its Equations
Equation of Plane Passing Through the Given Point
Foot of Perpendicular from a Point \[\mathbf{A(\alpha ,}\,\,\mathbf{\beta ,}\,\,\mathbf{\gamma )}\]to a given plane \[\mathbf{ax+by+cz+d=0}\].
Angle Between Two Planes
Equation of Planes Bisecting Angle Between Two Given Planes
Image of a Point in a Plane
Coplanar Lines
Equation of Plane Through a Given Line
Intersection Point of a Line and Plane
Angle Between Line and Plane
Projection of a Line on a Plane
General Equation of Sphere
Equation in Sphere in Various Forms
Section of a Sphere by a Plane
Condition of Tangency of a Plane to a Sphere
Intersection of Straight Line and a Sphere
Angle of Intersection of Two Spheres