Answer:
Step-by-step explanation:
The vertex and focus are horizon aligned, so the parabola is horizontal and the directrix is a vertical line.
The vertex is halfway between focus and directrix. Directrix: x = -4
The equation of directrix of the parabola will be x = -4.
Directrix is a straight line distance to which from any point of a conic section is in fixed ratio to the distance from the same point to a focus. The directrix is perpendicular to the axis of symmetry and does not touch the parabola.
We have,
Vertex of parabola = (0, 0),
Focus of the parabola = (4, 0),
Now,
The Equation of directrix is given by y = -a
Where,
The equation of the parabola, [tex]y^2 = 4ax[/tex],
And,
Focus at (a, 0),
i.e. a = 4 (As the given focus is (4, 0))
And,
The axis of the parabola is the positive x − axis.
So,
The equation of the directrix of this parabola,
x + a = 0,
i.e.
x + 4 = 0
⇒
x = -4
Hence, we can say that the equation of directrix of the parabola will be x = -4.
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