Question

Please help!!!
Write the equation of a parabola with a vertex at (-2,1), axis y=1, and latus rectum 4 units long.

Answer 1

I think this is the first time im hearing "latus rectum"

Answer 2

yeah what is that? lol

Answer 3

@Hero @ShailKumar

Answer 4

okay so i just googled it,
\[(x-(-2))^2=4(y-1)\]
the latus rectum would be the four part.

Answer 5

a little added help on parabolas

(x + 2)² = 4(y - 1)

Compare to this standard form:

(x - h)² = 4p(y - k)

which has these properties:

1. vertex is the point (h,k)
2. line of symmetry equation is x = h
3. focus is the point (h,k+p)
4. directrix is the line whose equation is y = k-p
5. length of latus rectum = |4p|

h = -2, k = 1, 4p = 4, so p = 1

So for this parabola,

1. vertex is the point (h,k) = (-2,1)
2. line of symmetry equation is x = h or x = -2
3. focus is the point (h,k+p) = (-2,1+1) = (-2,2)
4. directrix is the line whose equation is y = k-p
or y = 1-1 or y = 0, which is the x-axis.
5. length of latus rectum = |4p| = 4

Answer 6

ooh ok lol thanks!!!

Answer 7

The line segment L1L2 perpendicular to the axis of the parabola and passing through the focus is called latus rectum. It can be proved that its length is 4*|p|.