Respuesta :
Answer:
The equation of parabola is given by:
[tex](y-k)^2 = 4a(x-h)[/tex]
where,
(h, k) is the vertex.
Focus = (h+a, k)
As per the statement:
A parabola has a vertex at (0,0).
⇒[tex]y^2 = 4ax[/tex]
The focus of the parabola is located at (4,0).
⇒[tex](h+a, k) = (4, 0)[/tex]
⇒[tex](a, 0) = (4, 0)[/tex]
⇒a = 4
then, equation become:
[tex]y^2 = 16x[/tex]
We have to find the equation of directrix
The equation of directrix is, x = h-a
then;
x = 0-4 = -4
⇒x = -4
Therefore, the equation of directrix is, x = -4
