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4 years ago

Write the equation for a parabola with a focus at (-8, -1) and a directrix at y = − 4.

Mathematics

1 answer:

Sidana [21]4 years ago

4 0

Answer:

y = 1/6 x^2 + 8/3 x + 49/6

Step-by-step explanation:

This is a parabola which opens upwards.

The distance of a point (x, y) from the focus is

√[(x - -8)^2 + (y - -1)^2] and

the distance of the point from the line y = -4

= y - -4

These distances are equal for a parabola so:

√[(x - -8)^2 + (y - -1)^2] = y + 4

Squaring both sides:

(x + 8)^2 + (y + 1)^2 = (y + 4)^2

x^2 + 16x + 64 + y^2 + 2y + 1 = y^2 + 8y + 16

x^2 + 16x + 64 + 1 - 16 = 8y - 2y

6y = x^2 + 16x + 49

y = 1/6 x^2 + 8/3 x + 49/6 is the equation of the parabola.

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4 years ago

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1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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