What is the locus of points of intersection of a sphere and a plane ?

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

Show that the locus of the point of intersection of mutually perpendicular tangetns to a parabola is its directrix.

A variable plane passes through a fixed point(3,2,1) and meets and axes at A,B,C respectively. A plane is drawn parallel to plane through a second plane is drawn parallel to plane through A,B,C . Then the locus of the point of intersection of these three planes, is :

What is the maximum number of points of intersection of three lines in a plane? What is the minimum number?

What is the maximum number of points of intersection of three lines in a plane? What is the minimum number?

A variable plane passes through a fixed point (alpha,beta,gamma) and meets the axes at A,B, and C . show that the locus of the point of intersection of the planes through A,B and C parallel to the coordinate planes is alpha x^(-1)+beta y^(-1)+gamma z^(-1)=1