Problems from Reduced equation of the horizontal parabola

Development:

We choose $P(1,0)$.

First, the origin is the vertex, so $A(0,0)$ and it is a reduced equation. The point $P(1,0)$ is the focus $F({\displaystyle \frac{p}{2}},0)$, so ${\displaystyle \frac{p}{2}}=1$ and then $p=2$.

It is possible now to find the equation by substituting $p$ in $y^2=2px$. The equation is $$y^2=4x$$

To obtain the generator function we substitute $p$ in $x=-{\displaystyle \frac{p}{2}}$ and find the straight line $$x=-1$$

Solution:

For $P(1,0)$ the parabola is $y^2=4x$ and the generator line is $x=-1$.

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