Mathematics, 03.02.2020 00:59 10121545

to practice writing the equations of horizontal parabolas, write the equations of these two parabolas in vertex form:

focus at (4, 3), and directrix x = 2
focus at (2, -1), and directrix x = 8

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Answer from: 182075

Part a) the equation of parabola is: (y-3)^2 = 4(x-3)

Part b) the equation of parabola is: (y+1)^2 = -12 (x-5)

Step-by-step explanation:

Part a: focus at (4, 3), and directrix x = 2

Step 1: Find the horizontal or vertical direction

As the directrix x=2 is horizontal, we will use the equation of horizontal parabola i.e.

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

Step 2: Find the vertex (h,k)

The vertex (h,k) is between the directrix and the focus

x-coordinate (h) can be found by:

$h=\frac{x-coordinate of focus + directrix}{2}\\h= \frac{4+2}{2}\\h=\frac{6}{2}\\h=3$

the value y-coordinate (k) will be the same as the y-coordinate of focus i.e. k=3

so, vertex(h,k) =(3,3)

Step 3: Find the distance from focus to vertex

The distance from focus to vertex is denoted by p

and can be found by:

p= x-coordinate of focus-x-coordinate of vertex

p= 4 - 3

p= 1

Step 4: Putting values of vertex (h,k) and p in the equation.

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

(y-3)^2 = 4(1) (x-3)

(y-3)^2 = 4 (x-3)

so, the equation of parabola is: (y-3)^2 = 4(x-3)

Part b: focus at (2, -1), and directrix x = 8

Step 1: Find the horizontal or vertical direction

As the directrix x=8 is horizontal, we will use the equation of horizontal parabola i.e.

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

Step 2: Find the vertex (h,k)

The vertex (h,k) is between the directrix and the focus

x-coordinate (h) can be found by:

$h=\frac{x-coordinate of focus + directrix}{2}\\h= \frac{2+8}{2}\\h=\frac{10}{2}\\h=5$

the value y-coordinate (k) will be the same as the y-coordinate of focus i.e. k=-1

so, vertex(h,k) =(5,-1)

Step 3: Find the distance from focus to vertex

The distance from focus to vertex is denoted by p

and can be found by:

p= x-coordinate of focus-x-coordinate of vertex

p= 2 - 5

p= -3

Step 4: Putting values of vertex (h,k) and p in the equation.

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

(y-(-1))^2 = 4(-3) (x-5)

(y+1)^2 = -12 (x-5)

So the equation of parabola is: (y+1)^2 = -12 (x-5)

Answer from: Joejar63

Part a) the equation of parabola is: (y-3)^2 = 4(x-3)

Part b) the equation of parabola is: (y+1)^2 = -12 (x-5)

Step-by-step explanation:

Part a: focus at (4, 3), and directrix x = 2

Step 1: Find the horizontal or vertical direction

As the directrix x=2 is horizontal, we will use the equation of horizontal parabola i.e.

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

Step 2: Find the vertex (h,k)

The vertex (h,k) is between the directrix and the focus

x-coordinate (h) can be found by:

$h=\frac{x-coordinate of focus + directrix}{2}\\h= \frac{4+2}{2}\\h=\frac{6}{2}\\h=3$

the value y-coordinate (k) will be the same as the y-coordinate of focus i.e. k=3

so, vertex(h,k) =(3,3)

Step 3: Find the distance from focus to vertex

The distance from focus to vertex is denoted by p

and can be found by:

p= x-coordinate of focus-x-coordinate of vertex

p= 4 - 3

p= 1

Step 4: Putting values of vertex (h,k) and p in the equation.

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

(y-3)^2 = 4(1) (x-3)

(y-3)^2 = 4 (x-3)

so, the equation of parabola is: (y-3)^2 = 4(x-3)

Part b: focus at (2, -1), and directrix x = 8

Step 1: Find the horizontal or vertical direction

As the directrix x=8 is horizontal, we will use the equation of horizontal parabola i.e.

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

Step 2: Find the vertex (h,k)

The vertex (h,k) is between the directrix and the focus

x-coordinate (h) can be found by:

$h=\frac{x-coordinate of focus + directrix}{2}\\h= \frac{2+8}{2}\\h=\frac{10}{2}\\h=5$

the value y-coordinate (k) will be the same as the y-coordinate of focus i.e. k=-1

so, vertex(h,k) =(5,-1)

Step 3: Find the distance from focus to vertex

The distance from focus to vertex is denoted by p

and can be found by:

p= x-coordinate of focus-x-coordinate of vertex

p= 2 - 5

p= -3

Step 4: Putting values of vertex (h,k) and p in the equation.

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

(y-(-1))^2 = 4(-3) (x-5)

(y+1)^2 = -12 (x-5)

So the equation of parabola is: (y+1)^2 = -12 (x-5)

Answer from: Quest

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

Answer from: Quest

y=1/4x-4

step-by-step explanation:

Here’s a graph of a linear function. write the equation that describes that function

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to practice writing the equations of horizontal parabolas, write the equations of these two parabola...

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