Question

To which point the origin is to be shifted in order to remove the first degree terms in the equation $2x^2-3y^2-12x+18y-4=0$ is

• A. $(-3,-3)$
• B. $(3,3)$
• C. $(-3,3)$
• D. $(3,-3)$

Answer 1

The correct option is B $(3,3)$

Let origin be shifted to $(h,k)$
$(x^1,y^1)=(x-h,y-k)$
$\Rightarrow (x,y)=(x^1+h,y^1+k)$
$2(x^1+h{)}^2-3(y^1+k{)}^2-12(x^1+h)+18(y^1+k)-4=0$
To remove the first degree terms,
$\Rightarrow 2\left(2x^{1}h\right)-12x^1=0,-3\left(2y^{1}k\right)+18=0$
$h=3$

$k=3$
$\therefore (3,3)$ is shigted origin