Answer:
Step-by-step explanation:
The directrix y=-6 is parallel to the x axes, so parabola has equation of the form
where is the vertex of parabola and p is parabola's parameter.
By the definition, is the distance from the vertex to the directrix, so
Hence, the equation of parabola is
See attached diagram for the graph of parabola and its directrix.
In vertex form this equation is
This equation has the next form:
To find if the equation has two complex solutions we have to check if the discriminant is negative, as follows:
Then, the first case has two complex solutions.
In the second case,
The discriminant in this case is:
Then, the second case has two complex solutions.
In the third case,
The discriminant in this case is:
Then, the third case has two real solutions.
In the fourth case,
The discriminant in this case is:
Then, the fourth case has two complex solutions.