ANSWER
p=10
Opens up
Focus:(0,10)
Directrix: y=-10
EXPLANATION
The given parabola has equation;
[tex] {x}^{2} = 40y[/tex]
We compare this to
[tex] {x}^{2} = 4py[/tex]
This implies that,
[tex]4p = 40[/tex]
Hence,
[tex]p = 10[/tex]
Since p is positive, and the orientation is on the y-axis, the parabola opens up.
The coordinates of the focus are (0,p).
Hence the focus is (0,10).
The equation of the directrix is y=-p.
Therefore the directrix has equation,
[tex]y = - 10[/tex]
The features of the given parabola are; p = 10; It opens up; Focus at (0,10); Directrix at y = -10
The general form of equation of parabola is;
x² = 4py
We are given the equation of this parabola as x² = 40y
Thus;
4py = 40y
p = 40y/4y
p = 10
The value of p is positive and it will have its' orientation on the y-axis which means that the parabola opens up.
The coordinates of the focus are (0,p). Since p = 10, then;
The coordinates of the focus are; (0,10).
The equation of the directrix is given as; y =-p.
Thus, the directrix equation is; y = -10
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