Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.
1 answer:
Answer:
Step-by-step explanation:
The directrix intersects the x-axis at point (2,0). Points (-2,0) and (2,0) are symmetric about the origin, so the vertex of the parabola is placed at the origin (0,0).
The parameter p of the parabola is the distance from the focus to the directrix, thus p=4.
The branches of the parabola go in negative direction of x-axis, because the focus lies to the left from the vertex.
The equation of the parabola is
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Answer:
Step-by-step explanation:
the answer is explained in the picture
We have the following function:
So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
as shown in the Figure. This is also true because of 
where 
must be greater (or equal) than zero.
Second. The range of the function are the values of
.
Third. If creases then 
always creases, too.
So if we graph this function we will get the Figure below. Thus, let's study both the equation and the graph to get some conclusions. Therefore, we can assure these statements:
First. The function is defined only for
Second. The range of the function are the values of
Third. If