Discussion Forum

1)

In order to eliminate  the first degree terms from the equation

$4x^{2}+8xy+10y^{2}-8x-44y+14=0$ the point to which the origin has to be shifted is 

Answer:

Option A

Explanation:

On comparing the given equation with 

$ax^{2}+2hxy+by^{2}+2gx+2fy+c=0$ we get

 a=4,h=4, b=10,g=-4, f=-22 and c=14

 For removal of first degree terms , shift  the origin to

 $\left(\frac{bg-fh}{h^{2}-ab},\frac{af-gh}{h^{2}-ab}\right)=\left(\frac{-40+88}{16-40},\frac{-88+16}{16-40}\right)$

$=\left(\frac{48}{-24},\frac{-72}{-24}\right)=(-2,3)$