Q. 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)
Explanation
(c)
Here, $a = 2,\ b = 5,\ c = 7,\ h = 2,\ g = - 2,\ f = - 11$
To eliminate 1st degree terms origin is to be shifted to the point
$\left( \frac{hf - bg}{ab - h^{2}},\frac{gh - af}{ab - h^{2}} \right) = \left( \frac{- 22 + 10}{10 - 4},\frac{- 4 + 22}{10 - 4} \right) = ( - 2,\ 3)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.