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marusya05 [52]
3 years ago
6

Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

Mathematics
1 answer:
7nadin3 [17]3 years ago
3 0

Answer:

y^2=-8x

Step-by-step explanation:

The directrix intersects the x-axis at point (2,0). Points (-2,0) and (2,0) are symmetric about the origin, so the vertex of the parabola is placed at the origin (0,0).

The parameter p of the parabola is the distance from the focus to the directrix, thus p=4.

The branches of the parabola go in negative direction of x-axis, because the focus lies to the left from the vertex.

The equation of the parabola is

(y-0)^2=-2\cdot 4\cdot (x-0),\\ \\y^2=-8x.

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