Question

A point moves so that its distances from the points (3, 4, –2) and (2, 3, – 3) remains equal. The locus of the point is

• A. A line
• B. A plane whose normal is equally inclined to axes
• C. A plane which passes through the origin
• D. A sphere

Answer 1

Answer: (B)

A plane whose normal is equally inclined to axes

Answer 2

According to question,

$( x - 3 ) ^ { 2 } + ( y - 4 ) ^ { 2 } + ( z + 2 ) ^ { 2 } = ( x - 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } + ( z + 3 ) ^ { 2 }$

$\therefore$ The equation reduces to a plane as 2^nd degree terms cancel out.

The equation is $2 x + 2 y + 2 z = 7$ hence equally inclined to axes.