Answer:
x² = +/- 12y and y² = +/- 12x
p=-3
CD=28
Step-by-step explanation:
The two possible equations for a parabola:
(x-h)² = +/- 4c(y-k) and (y-k)² = +/- 4c(x-h),
where
(h,k) = vertex coordinates
c = distance of the focus from the vertex
+/- indicates the parabola opens downwards(-) or upwards(+) in case it passes through x-axis or to the left(-) or to the right(+) in case it passes through y-axis
As given, vertex is at the origin, so the (h,k) are (0,0).
That means h=0 and k=0. Also, the focus c=3.
The two possible equations for given parabola:
x² = +/- 12y and y² = +/- 12x
B.
in case ofy² = +/- 12x
directrix =h-p
=0-(-3)
=3
in case of x² = +/- 12y
directrix=k-p
=0-(-3)
=3
C.
In given parabola, the vertex is at (0,0). line CD is parallel to directrix that is running through the new focus of the parabola i.e at 7 now. CD intersects parabola at two points C and D on either side of the focus. This distance CD is called focal width given by 4p.
CD=4p = 4(7) = 28 !
