Question

Please solve this, pls ignore the marked words with a line :)

Answer 1

`\begin{gathered} 4\cdot(1)/(2)\cdot(x-2)=(y-1)^2 \\ \text{ Focus }=((5)/(2),1) \\ \text{ Vertex = }(2,1) \\ \text{ Directrix = }(3)/(2) \end{gathered}`

Explanation:

We have the following function:

`-2x+y^2-2y+5=0`

We convert it to its standard form as follows:

`\begin{gathered} 2x=y^2-2y+5 \\ x=(y^2)/(2)-(2y)/(2)+(5)/(2) \\ x=(1)/(2)\cdot(y-1)^2+2 \\ 2\cdot(x-2)=(y-1)^2 \\ 4\cdot(1)/(2)\cdot(x-2)=(y-1)^2 \end{gathered}`

Now, starting from the standard form, we can define the focus, the vertex and the directrix:

`\begin{gathered} \text{ Focus }=((5)/(2),1) \\ \text{ Vertex = }(2,1) \\ \text{ Directrix = }(3)/(2) \end{gathered}`