Question

The focus of the curve $y^2+4x-6y+13=0$ is

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

Answer 1

Answer: (B)

The given equation of curve is :
$y^2+4x-6y+13=0$
which can be written as : $y^2-6y+9+4x+4=0$
$\Rightarrow \left(y^2-6y+9\right)=-4\left(x+1\right)$
$\Rightarrow {\left(y-3\right)}^2=-4\left(x+1\right)$
Put $Y=y-3$ and $X=x+1$
On comparing $Y^2=4aX$
Length of focus from vertex, $a=-1$
At focus $X=a$ and $Y=0\Rightarrow x+1=-1$
$\Rightarrow x=-2$
$\therefore y-3=0\Rightarrow y=3$
$\therefore$ Focus is $\left(-2,3\right).$