Question
Graph the parabolas and identify the axis, directrix, and focus: (y^2)+8x=0
I know that the axis refers to the axis of symetry and the directrix is the same distance away from the vertex as the foucus is. I just don't know how to graph and identify all the parts from an equation like the one above.
I know that the axis refers to the axis of symetry and the directrix is the same distance away from the vertex as the foucus is. I just don't know how to graph and identify all the parts from an equation like the one above.
Answers
Steve
Recall that the parabola
y^2 = 4px
has
vertex at (0,0)
focus at (p,0)
directrix at x = -p
(y^2)+8x=0
can be written as
y^2 = -8x
so p = -2
now just plug and chug.
It is clearly a parabola opening to the left with vertex at (0,0).
y^2 = 4px
has
vertex at (0,0)
focus at (p,0)
directrix at x = -p
(y^2)+8x=0
can be written as
y^2 = -8x
so p = -2
now just plug and chug.
It is clearly a parabola opening to the left with vertex at (0,0).
Anonymous
Thank you so much Steve!! just two questions, what does the variable "p" stand for/ represent and could I be able to represent the axis of symetry as an equation/point.
Anonymous
wait dose the axis even mean the axis of symetry??
Steve
yes, "axis" means the axis of symmetry.
and yes, your parabola has the x-axis as its axis of symmetry.
y = 0
and yes, your parabola has the x-axis as its axis of symmetry.
y = 0
Anonymous
thanks you so much!!
Gerald Zea
Can someone help me please.
How to find the equation of the axis of parabola and its length of the latus rectum having y-x²+8x=0?
How to find the equation of the axis of parabola and its length of the latus rectum having y-x²+8x=0?