Mathematics, 17.05.2021 09:00 preety5445

The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?

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Answer from: cp838761

The equation of the parabola is $y = -12\cdot x^{2}$ .

Step-by-step explanation:

Since the directrix is of the form y = a , the parabola is vertical. The vertex of the parabola ( V(x,y) ) is the midpoint between the focus ( F(x,y) ) and a point of the directrix ( P(x,y) ), that is to say:

$V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y)$ (1)

If we know that F(x,y) = (0, -3) and P(x,y) = (0, 3) , then the coordinates of the vertex of the parabola:

$V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)$

V(x,y) = (0, 0)

The vertex factor () is the distance of the focus with respect to the vertex:

$p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]}$ (2)

If we know that F(x,y) = (0, -3) and V(x,y) = (0, 0) , then the vertex factor is:

$p = \sqrt{0^{2}+(-3)^{2}}$

p = -3

The equation of the parabola in the vertex form is described below:

$y - k = 4\cdot p \cdot (x-h)^{2}$ (3)

Where:

- Independent variable.

- Dependent variable.

h, k - Coordinates of the vertex.

If we know that (h,k) = (0, 0) and p = -3 , then the equation of the parabola is $y = -12\cdot x^{2}$ .

The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?

Answer from: Quest

whatare you sayig

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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