Find the radius of the circular section of the sphere by the plane
The equation of the sphere is
∴ Centre and radius of the sphere are (0, 0, 0) and 5 respectively.
The equation of the plane is
OA = length of perpendicular from the origin to the plane
∴ Given plane intersects the sphere.
∴ Radius of the circular section of the sphere is 4.
Find the centre and radius of the sphere
Find the equation of the sphere concentric with the sphere
and double its radius.
A point P(x, y, z) is such that 3PA = 2PB, where A and B are the points (1, 3, 4) and (1, – 2, –1) respectively. Find the equation of the locus of the point P and show that the locus is a sphere.
Find the equation of the sphere whose centre has the position vector and which touches the plane
Find the value of for which the plane touches the sphere
Find the centre and radius of the circle in which the plane intersects the sphere
Find the equation of the sphere passing through the points (0, 0, 0), (–1, 2, 0), (0, 1, –1) and (1, 2, 5).
Find the equation of the sphere which passes through the points (1,–3, 4), (1, –5, 2), (1, –3, 0) and has its centre on the plane x + y + z = 0.