Find the condition for which the plane lx+my+nz=0 touches the sphere x2+y2+z2+2ux+2vy+2wz = 0 Share with your friends Share 2 Manbar Singh answered this A plane will touch the sphere if the length of the perpendicular drawn from the centreof the sphere to the plane is equal to radius of sphere.The equation of the given sphere is,x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 ....1Now, centre of the given sphere is -u, -v, -w and the radius is u2+ v2 + w2 - dNow, length of the ⊥ drawn from point -u, -v, -w to the plane lx+my+nz = p is given by, d = l-u + m-v + n-w - dl2 + m2 + n2⇒d = lu+mv+nw+dl2 + m2 + n2Now, d = radius of sphere⇒lu+mv+nw+dl2 + m2 + n2 = u2+ v2 + w2 - d⇒lu+mv+nw+d2 = l2 + m2 + n2u2+ v2 + w2 - dThis is the required condition. -1 View Full Answer