Question

The centre of the conic represented by the equation $x^2-6xy+y^2+6x+14y-2=0$ is

• A. $(3,2)$
• B. $(3,4)$
• C. $(-3,4)$
• D. $(5,4)$

Answer 1

The correct option is A $(3,2)$

Let $f(x,y)=x^2-6xy+y^2+6x+14y-2=0$
Partially differentiate w.r.t. $x$ and equate to zero
$\frac{\delta f}{\delta x}=2x-6y\cdot 1+0+6+0+0=0$ (treat $y$ as constant)
$\Rightarrow x-3y+3=0\cdots \left(1\right)$

Again, partially differentiate w.r.t. $y$ and equate to zero
$\frac{\delta f}{\delta y}=-6x+2y+14=0$ (treat $x$ as constant)
$\Rightarrow y-3x+7=0\cdots \left(2\right)$
Solving $\left(1\right)$ and $\left(2\right),$
$x=3$ and $y=2$
$\therefore$ Centre of given conic is $(3,2)$