Question

The focus of the parabola $x^2-8x+2y+7=0$ is:

• A. $(0,-\frac{1}{2})$
• B. $(4,4)$
• C. $(4,\frac{9}{2})$
• D. $(-4,-\frac{9}{2})$

Answer 1

The correct option is B $(4,4)$

$x^2-8x+2y+7=0$
$x^2-8x+16=-2y+9$
$(x-4{)}^2=-2(y-\frac{9}{2})$
Thus focus of the parabola is, $x-4=0\Rightarrow x=4,y-\frac{9}{2}=-\frac{1}{2}\Rightarrow y=4$