A parabola has a vertex at (0,0). The focus of the parabola is located at (4,0). What is the equation of the directrix?
Answer:
The equation of parabola is given by:
\((y-k)^2 = 4a(x-h)\)
where,
(h, k) is the vertex.
Focus = (h+a, k)
As per the statement:
A parabola has a vertex at (0,0).
⇒\(y^2 = 4ax\)
The focus of the parabola is located at (4,0).
⇒\((h+a, k) = (4, 0)\)
⇒\((a, 0) = (4, 0)\)
⇒a = 4
then, equation become:
\(y^2 = 16x\)
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