I am suppose to graph this conic section how do I do this equation
You must learn all the various forms for
all the various conic sections, and all their
properties.
This one can be placed in standard form:
which is a parabola with a horizontal axis of
symmetry with vertex = (h,k),
distance from vertex to focus and directrix = |p|
which opens right if p is positive and left if p is negative.
Now we put your equation in standard form:
Swap sides:
Multiply both sides by
Compare to the general standard form:
and we have , ,
So the vertex is (h,k) = (-2,1) and
and since p is positive the parabola opens to
the right.
So we plot the vertex (-2,1)
and the axis of symmetry is the horizontal line through the vertex,
whose equation is
We'll draw it in blue:
Since , and since it is positive, the focus
is of a unit to the right of the vertex, or the point
(,1) = (,1) = (,1)
So we plot the focus, but unfortunately, it's so close
to the vertex, it's hard to plot it so it doesn't run
into the vertex.
Now we draw the directrix which is a vertical line of a unit to the left of the vertex. Its equation is
We'll draw it in green:
Next we draw a horizontal line from the focus directly through
the vertex to the directrix. Unfortunately you can hardly see it
because it's so short because those points are so close together:
Draw a square on each side of that line. They too are unfortunately
very tiny in this problem:
Now we can find the y-intercepts by letting x = 0 in the
original equation and solving for y
±
This gives the y-intercepts at about (0,1.7) and (0.3)
So we plot those:
Finally we draw the parabola through the right corners of the
squares, through the vertex and through the y-intercepts:
That's it. It's too bad the parabola you picked to plot had
such a tiny value of p.
Edwin