Question

In order to eliminate the first degree terms in the equation $2x^2-2y^2+z^2-4x+8y+2z-5=0$, then origin should be shifted to the point

• A. $(1,2,1)$
• B. $(1,2,-1)$
• C. $(-1,2,1)$
• D. $(1,-2,1)$

Answer 1

The correct option is B $(1,2,-1)$

The equation $2x^2-2y^2+z^2-4x+8y+2z-5=0$ can also be written as

$2{(x-1)}^2-2{(y-2)}^2+{(z+1)}^2=0$ ....(1)
If we define a new coordinate system $X-Y-Z$ such that
$x-1=X,y-2=Y,z+1=Z$,
Then, the equation (1) reduces to,
$2X^2-2Y^2+Z^2=0$

Which is independent of first degree terms.

$x=X+1,y=Y+2,z=Z-1$.
Hence, the coordinates of the new origin are: $(1,2,-1)$

Hence, option B is correct.