Question

Centre of the ellipse $5x^2-6xy+5y^2+22x-26y+29=0$ is

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

Answer 1

Answer: (D)

$(-1,2)$

Centre of ellipse is $(\frac{\delta s}{\delta x}=0,\frac{\delta s}{\delta y}=0)$
$\frac{\delta s}{\delta x}=0\Rightarrow 10x-6y+22=0$
$\frac{\delta s}{\delta y}=0\Rightarrow 10y-6x-26=0$
Solving both eqns
$\Rightarrow x=-1;y=2$
$\therefore$centre is $(-1,2)$