Question

For the given parabola $x^2+2y=8x-7$ which of the following is/are correct?

• A. axis will be $2y=9$
• B. axis will be $x=4$
• C. vertex will be $(4,\frac{9}{2})$
• D. vertex will be $(\frac{9}{2},4)$

Answer 1

Answer: (B), (C)

The correct options are
B axis will be $x=4$
C vertex will be $(4,\frac{9}{2})$

We have $x^2-8x=-2y-7$
$\Rightarrow (x-4{)}^2=-2(y-\frac{9}{2})$
Clearly the vertex is $(4,\frac{9}{2})$.
Now shifting the origin to $(4,\frac{9}{2})$
We get the equation as $X^2=-2Y$
For this parabola axis will be $X=0\Rightarrow x=4$