The locus of the equation (x^{2} + y^{2} + z^{2} + 1 = 0)is | MATH - SYSTEM OF CO-ORDINATES, DIRECTION COSINES & DIRECTION RATIOS, PROJECTION | SolveeIt | Solveeit

Today, August 18

Question

The locus of the equation $x^{2} + y^{2} + z^{2} + 1 = 0$ is

A

An empty set

B

A sphere

C

A degenerate set

D

A pair of planes

Answer

An empty set

Explanation

Solution

An empty set. $\left( \because x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 1 = 0 \right.$ is not possible for any real value of x)