HEEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPP
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(8)
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(9)
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(10)
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(11)
we can plug it
(12)
we can plug it
(13)
we can replace g(x)
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(14)
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Well, "<span>the set of all points in the plane equidistant from the focus and a line", is referring to the focus point of the parabola and the directrix line.
bearing in mind that, both fellows are at a distance "p" from the vertex, that puts the vertex right in the middle of them.
notice, the focus point is below the directrix, meaning, is a vertical parabola, and is also opening downwards, like in the picture below.
from -5 to 5 over the y-axis, there are 10 units, so the "p" distance is 5, so that puts the vertex right at the origin.
since the parabola is opening downwards, "p" is negative, thus -5.
</span>
<span>
</span>
bearing in mind that, both fellows are at a distance "p" from the vertex, that puts the vertex right in the middle of them.
notice, the focus point is below the directrix, meaning, is a vertical parabola, and is also opening downwards, like in the picture below.
from -5 to 5 over the y-axis, there are 10 units, so the "p" distance is 5, so that puts the vertex right at the origin.
since the parabola is opening downwards, "p" is negative, thus -5.
</span>
</span>