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Umnica [9.8K]
3 years ago
5

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?

Mathematics
2 answers:
UkoKoshka [18]3 years ago
5 0
The equation is y^2=16x and the directrix is x=-4
Travka [436]3 years ago
3 0

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

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