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

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.

d

step-by-step explanation:

the 2000 florida legislature amended section 322.05, florida statutes, changing the requirements to obtain a class e license for a driver under the age of 18 holding a learner's license. the following requirements must be met in order to obtain a regular class e license if a learner's license is issued on or after october 1, 2000:

must hold a learner's license for at least 12 months or until the 18th birthday.

must have no convictions 12 months from the issue date of the learner's license.

may have one traffic conviction within 12 months from the issue date of the learner's license if adjudication is withheld.

a parent, legal guardian, or responsible adult over 21 years old must certify that the driver has 50 hours driving experience, including 10 hours of night time driving.