Question

help

Answer 1

@oliver69

Answer 2

Why don't you ask the teacher for help

Answer 3

The equation of a parabola is \[x=\frac{ 1 }{ 4(f−h) }(y−k)^2+h\], where (h,k) is the vertex and (f,k) is the focus.

Thus, h=0, k=0.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f−h=h−8/3​.

Solving the system {h=0, k=0, f−h=h−83

we get that h=0, k=0, f=−8/3​

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y=0.

The focal length is the distance between the focus and the vertex: 8/3.

The focal parameter is the distance between the focus and the directrix: 16/3

The latus rectum is parallel to the directrix and passes through the focus: x=−8/3

The endpoints of the latus rectum can be found by solving the system {3/2x+3y^2=0

The endpoints of the latus rectum are (−8/3,−16/3)(-8/3,16/3)

The length of the latus rectum (focal width) is four times the distance between the vertex and the focus: 32/3

The eccentricity of a parabola is always 1

The x-intercepts can be found by setting y=0 in the equation and solving for x

x-intercept: (0,0)

The y-intercepts can be found by setting x=0 in the equation and solving for y:

y-intercept: (0,0)

In standard form the answer is \[x=−\frac{ 3y^2 }{ 32 }\]



(Fyi I'm glad I can help and I don't care what other's say lol)

Answer 4

says it's not right