232k views
3 votes
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?

User Liamvictor
by
8.1k points

2 Answers

2 votes
the equation is y^2=16x and the directrix is x=-4
User Integer Poet
by
7.8k points
7 votes

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

User Cleve
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories