Q98 / 160 · TS EAMCET 2017 · Mathematics
In order to eliminate the first degree terms from the equation $4 x^2+8 x y+10 y^2-8 x-44 y+14=0$ the point to which the origin has to be shifted is
- Correct answerA$(-2,3)$
- B$(2,-3)$
- C$(1,-3)$
- D$(-1,3)$
Solution
On comparing the given equation with
$$
\begin{aligned}
& a x^2+2 h x y+b y^2+2 g x+2 f y+c=0, \text { we get } \\
& a=4, h=4, b=10, g=-4, f=-22 \text { and } c=14
\end{aligned}
$$
For removal of first degree terms, shift the origin to
$$
\begin{aligned}
\left(\frac{b g-f h}{h^2-a b}, \frac{a f-g h}{h^2-a b}\right) & =\left(\frac{-40+88}{16-40}, \frac{-88+16}{16-40}\right) \\
& =\left(\frac{48}{-24}, \frac{-72}{-24}\right)=(-2,3)
\end{aligned}
$$
Hence, the correct answer is option: 'A'.