The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.

Find the equation of the sphere described on the joint of points Aa n dB having position vectors 2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k , respectively, as the diameter. Find the center and the radius of the sphere.

Three metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted together to form a single solid sphere. Find the radius ofthe resulting sphere.

Let a given line L_1 intersect the X and Y axes at P and Q respectively. Let another line L_2 perpendicular to L_1 cut the X and Y-axes at Rand S, respectively. Show that the locus of the point of intersection of the line PS and QR is a circle passing through the origin

Find the diameter of a sphere whose surface area is 154m^(2) .

The curved surface area of a sphere of radius 5, intercepted between two paeallel planes of distance 2 and 4 from the centre is

Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2-y=z+3.

Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2-y=z+3.

Find the number of sphere of radius r touching the coordinate axes.

Line AB passes through point (2,3) and intersects the positive x and y-axes at A(a,0) and B(0,b) respectively. If the area of DeltaAOB is 11. then the value of 4b^2+9a^2 is