Question

In order to eliminate the first degree terms from the equation $2x^2+4xy+5y^2-4x-22y+7=0$, the point to which origin is to be shifted is

• A. $(1,-3)$
• B. $(2,3)$
• C. $(-2,3)$
• D. $(1,3)$

Answer 1

The correct option is C $(-2,3)$

Given the equation,

$S=2x^2+4xy+5y^2-4x-22y+7=0$

on partial differentiation and we get

$\frac{\delta s}{\delta x}=4x+4y-4=0$ ………$\left(1\right)$

$\frac{\delta s}{\delta y}=4x+10y-22=0$ ………..$\left(2\right)$

Solving from $\left(1\right)$ and $\left(2\right)$ to,

$4x+4y-4=0$

$4x+10y-22=0$

________________

$-6y+18=0$

$-6y=-18$

$y=3$

Put the value of y in equation $\left(1\right)$

$4x+4y-4=0$

$4x+4\times 3-4=0$

$4x+12-4=0$

$4x+8=0$

$4x=-8$

$x=-2$

Then point $(x,y)=(-2,3)$

Hence, this is the answer.