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

aortiH 2021-03-06 Answered
If the directrix is horizontal, then the parabola opens (horizontally/vertically)
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Expert Answer

jlo2niT
Answered 2021-03-07 Author has 96 answers

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:
y=ax2+bx+c(a0)
Step 2
The above equation is parabola opening upward if a>0 and opening downward if a<0.
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 xhandyk, then the graph of the parabola is shifted h units horizontally and k units vertically. The vertex is (h, k), and the focus is (h,k+p).
The directrix is the line defined by the equation y=kp and the equation of the parabola is:
(xh)2=4p(yk)
Step 4
The equation of directrix y=kp is horizontal. So, the parabola opens towards vertically.
Thus, the missing word is Vertically.

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