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joja [24]
2 years ago
12

Write an equation for a parabola in which the set of all points in the plane are equidistant from the focus and line F(-6,0); x=

6

Mathematics
1 answer:
Bogdan [553]2 years ago
3 0

Step-by-step explanation:

Since we have a vertical directrix, the equation of the parabola is

(y - k) {}^{2}  = 4p(x - h)

Where p is the distance from the vertex to the directrix.

or the distance from the vertex to the focus.

Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.

\frac{ - 6 + 6)}{2}  = 0

\frac{0 + 0}{2}  = 0

So our vertex is (0,0).

So our equation become

{y}^{2}  = 4px

The distance from the focus and directrix is 6.

So p=6.

{y}^{2}  = 24x

So p is 6.

Since p is 6,

\frac{ {y}^{2} }{24}  = x

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