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iris [78.8K]
3 years ago
10

Write an equation of the parabola with focus (0, -3) and vertex at the origin. Use z for the independent variable.

Mathematics
1 answer:
olchik [2.2K]3 years ago
4 0

Answer:

z^2 = -12y

or y = -(z^2/12)

Step-by-step explanation:

Answer:

z^2 = -12y

Step-by-step explanation:

Given the vertex at origin;

This is same as (0,0)

The focus (0,-3)

The general form is;

(z-h)^2 = 4p(y-k)

(h,k) is the vertex (0,0); so h = 0 and k = 0

The focus is given as;

(h,k + p)

so ;

k + p = -3

but k =0

so p = -3

Thus, the equation of the parabola is;

(z-0)^2 = 4(-3)(y-0)

z^2 = -12y

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