If the directrix is horizontal, then the parabola opens (text{horizontally}/text{vertically})

Question
Conic sections
asked 2021-03-06
If the directrix is horizontal, then the parabola opens \((\text{horizontally}/\text{vertically})\)

Answers (1)

2021-03-07
Step 1
Given:
We must find the missing word in the given sentence.
So, Definition of parabola said:
A parabola is another type of conic section generated by the cross section of a cone intersected by a plane.
An equation of the form:
\(\displaystyle{y}={a}{x}^{2}+{b}{x}+{c}{\left({a}\ne{0}\right)}\)
Step 2
The above equation is parabola opening upward if \(\displaystyle{a}>{0}\) and opening downward if \(\displaystyle{a}<{0}.\)</span>
So, the geometrically definition of parabola is the set of all points in a plane that the equidistant from a fixed line called directrix and a fixed point called the focus.
Step 3
In the standard form of a parabola, if x and y are replaced by \(\displaystyle{x}-{h}{\quad\text{and}\quad}{y}-{k}\), then the graph of the parabola is shifted h units horizontally and k units vertically. The vertex is (h, k), and the focus is \(\displaystyle{\left({h},{k}+{p}\right)}.\)
The directrix is the line defined by the equation \(\displaystyle{y}={k}-{p}\) and the equation of the parabola is:
\(\displaystyle{\left({x}-{h}\right)}^{2}={4}{p}{\left({y}-{k}\right)}\)
Step 4
The equation of directrix \(\displaystyle{y}={k}-{p}\) is horizontal. So, the parabola opens towards vertically.
Thus, the missing word is Vertically.
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