Question

The vertex of the parabola $x^2+2y=8x-7$ is

• A. $(\frac{9}{2},0)$
• B. $(4,\frac{9}{2})$
• C. $(2,\frac{9}{2})$
• D. $(4,\frac{7}{2})$

Answer 1

The correct option is B $(4,\frac{9}{2})$

Given equation of parabola is
$x^2+2y=8x-7$
$\Rightarrow x^2-8x=-2y-7$
$\Rightarrow x^2-8x+16=-2y-7+16$
$\Rightarrow {(x-4)}^2=-2(y-\frac{9}{2})$
$\therefore$ Vertex of the parabola is $(4,\frac{9}{2})$.