Question

The focus of the parabola $y^2+6x-2y+13=0$ is at the point

• A. $\left(\frac{7}{2},1\right)$
• B. $\left(\frac{-1}{2},1\right)$
• C. $\left(-2,\frac{1}{2}\right)$
• D. $\left(-\frac{7}{2},1\right)$
• E. $\left(-\frac{1}{2},-1\right)$

Answer 1

Answer: (D)

Given, $y^2+6x-2y+13=0$ $(y^2-2y+1)=-6x-12$ ${(y-1)}^2=-6(x+2)$ Let $y=y-1$ and $X=x+2$ then, $Y^2=-6X$ ...(i) Which is equation of parabola whose vertex is $(1,-2)$ and $\left(a=\frac{3}{2}\right)$ Now, focus
$=(-a-2,1)$
$=\left(\frac{-3}{2}-2,1\right)$
$=\left(-\frac{7}{2},1\right)$