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2 years ago

30 POINTS - PLEASE HELP

Mathematics

2 answers:

Ludmilka [50]2 years ago

7 0

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

in case ofy² = +/- 12x

directrix =h-p

=0-(-3)

in case of x² = +/- 12y

directrix=k-p

=0-(-3)

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 !

Tom [10]2 years ago

4 0

Answer:

1. x² = +/- 12y and y² = +/- 12x

2. p=-3

3. CD=28

Step-by-step explanation:

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