Find the equation for the parabola described it's vertex , directrix and focus . Vertex=(-e,-e) directrix=y= -2e focus=(-e,0)

Given: Vertex=(-e,-e), directrix: y= -2e, focus=(-e,0) (y-k) = (1/4a)(x-h)^2 Where (h,k) is the vertex, a is the distance from the vertex to the focus (and from the vertex to the directrix), and e is the distance from the vertex to the focus. h = -e k = -e a = e e = a/2 Therefore, substituting these values in the vertex form, we get: (y+e) = (1/4e)(x+e)^2 x^2 = 4ey x^2 = 2ay Therefore, the equation of the parabola is x^2 = 2ay.

Question

Asked 3/16/2016 4:44:25 AM

Updated 361 days ago|4/30/2023 12:15:45 AM

1 Answer/Comment

f
freestar.config.enabled_slots.push({ placementName: 'weegy_incontent_1', slotId: 'weegy_incontent_1' });

Rating

3

Given: Vertex=(-e,-e), directrix: y= -2e, focus=(-e,0)

(y-k) = (1/4a)(x-h)^2

Where (h,k) is the vertex, a is the distance from the vertex to the focus (and from the vertex to the directrix), and e is the distance from the vertex to the focus.

h = -e

k = -e

a = e

e = a/2

Therefore, substituting these values in the vertex form, we get:

(y+e) = (1/4e)(x+e)^2

x^2 = 4ey

x^2 = 2ay

Therefore, the equation of the parabola is x^2 = 2ay.

Added 361 days ago|4/30/2023 12:15:45 AM

This answer has been confirmed as correct and helpful.

Allyii
11 months ago
Find an equation for the parabola described by its vertex, directrix, and focus point:
vertex (-e, -e); directrix y =-2e; focus (-e, 0)
(y+e)^2 = 4e(x+e)
(x-e)^2 = 4e(y-e)
(x+e)^2 = 4e(y+e)
(y-e)^2 = 4e(x-e)

(y + e)^2 = 4e(x + e)

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

Question

Not Answered

Updated 361 days ago|4/30/2023 12:16:06 AM

1 Answer/Comment

(y + e)^2 = 4e(x + e)

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

Added 361 days ago|4/30/2023 12:16:06 AM

This answer has been confirmed as correct and helpful.

Rated good by Aj25

Find an equation for the parabola described by its vertex, directrix, and focus point:
vertex (-e, -e); directrix y =-2e; focus (-e, 0)
(y+e)^2 = 4e(x+e)
(x-e)^2 = 4e(y-e)
(x+e)^2 = 4e(y+e)
(y-e)^2 = 4e(x-e)

Question

Not Answered

Updated 334 days ago|5/27/2023 12:53:52 AM

2 Answers/Comments

(y + e)^2 = 4e(x + e)

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

Added 334 days ago|5/27/2023 12:53:47 AM

This answer has been confirmed as correct and helpful.

(y + e)^2 = 4e(x + e)

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

or

y^2 + 2ey + e^2 = 4ex + 4e^2

This is because the directrix is a horizontal line and the focus is on the negative side of the y-axis, which means the parabola opens to the left. Therefore, the equation should have the form (y + k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

Added 334 days ago|5/27/2023 12:53:52 AM

This answer has been added to the Weegy Knowledgebase

Find the equation for the parabola described it's vertex , directrix and focus **Weegy:** Hello how are you? **User:** Find the equation for the parabola described it's vertex , directrix and focus . Vertex=(-e,-e) directrix=y= -2e focus=(-e,0) (More)

Question

Updated 334 days ago|5/27/2023 12:54:39 AM

1 Answer/Comment

(x + e)^2 = 4e^2y + 4e^3. is the equation for the parabola described it's vertex , directrix and focus . Vertex=(-e,-e) directrix=y= -2e focus=(-e,0).

(x - h)^2 = 4p(y - k),

(x + e)^2 = 4p(y - k)

(x + e)^2 = 4p(y + p)

(x + e)^2 = 4e^2(y + e)

(x + e)^2 = 4e^2y + 4e^3

Thus, the equation for the parabola is:

(x + e)^2 = 4e^2y + 4e^3.

(x - h)^2 = 4p(y - k),

(x + e)^2 = 4p(y - k)

(x + e)^2 = 4p(y + p)

(x + e)^2 = 4e^2(y + e)

(x + e)^2 = 4e^2y + 4e^3

Thus, the equation for the parabola is:

(x + e)^2 = 4e^2y + 4e^3.

Added 334 days ago|5/27/2023 12:54:39 AM

This answer has been confirmed as correct and helpful.

39,079,390

questions answered

There are no comments.