Question

The co-ordinates of the points A and B are (2, 3, 4), (–2, 5,– 4) respectively. If a point P moves so that $P{A}^2-P{B}^2=k$ where k is a constant, then the locus of P is

• A. A line
• B. A plane
• C. A sphere
• D. a conic

Answer 1

The correct option is B A plane

$\because P{A}^2-P{B}^2=k\therefore \left[\right(x-2{)}^2+(y-3{)}^2+(z-4{)}^2]-[(x+2{)}^2+(y-5{)}^2+(z+4{)}^2]=k$
or -8x+4y-16z-16=k,which is the equation of a plane.