Question

Least number of changes for the expression $a{x}^2+bxy+c{y}^2+dx+ey+f$ to be symmetric in x and y is

• A. $a=b,c=d$
• B. $b=c,e=f$
• C. $a=c,d=e$
• D. $a=f,b=e,c=d$

Answer 1

The correct option is C $a=c,d=e$

$a{x}^2+bxy+c{y}^2+dx+ey+f$.......(1)

Replace by $x$ by $y$ and $y$ by $x$

$\Rightarrow a{y}^2+byx+c{x}^2+dy+ex+f$.......(2)

if (1) and (2) are equal then

$a=candd=e$