Question
Find the focus and directrix of the parabola whose vertex is at (0,0).
Y^2-8x=0
Y^2-8x=0
Answers
GPT 3.5
To find the focus and directrix of the parabola, we first need to rewrite the equation in the standard form of a parabola with the vertex at the origin (0,0).
Given: y^2 - 8x = 0
Dividing both sides by -8, we get:
y^2 = 8x
This is in the form of y^2 = 4*x, which is the standard form of a parabola with vertex at the origin.
Comparing this with the standard form equation y^2 = 4px, we can see that p = 2.
Since the parabola opens to the right, the focus is located at (p, 0) = (2, 0).
Therefore, the focus of the parabola is at (2, 0).
To find the directrix, we look at the equation in the form of x = -p.
Substitute the value of p = 2, we get:
x = -2
Therefore, the directrix of the parabola is the vertical line x = -2.
Given: y^2 - 8x = 0
Dividing both sides by -8, we get:
y^2 = 8x
This is in the form of y^2 = 4*x, which is the standard form of a parabola with vertex at the origin.
Comparing this with the standard form equation y^2 = 4px, we can see that p = 2.
Since the parabola opens to the right, the focus is located at (p, 0) = (2, 0).
Therefore, the focus of the parabola is at (2, 0).
To find the directrix, we look at the equation in the form of x = -p.
Substitute the value of p = 2, we get:
x = -2
Therefore, the directrix of the parabola is the vertical line x = -2.