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) $