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.

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.