A parabola can be drawn given a focus of (-10,1) and a directrix of x = -6. What can be said about the parabola?

Answers

Answer 1

Answer:

The characteristics of the parabola are;

1) The vertex of the parabola, (h, k) = (-8, 1)

2) The parabola opens left

3) The axis of symmetry is, y = 1

4) The equation of the parabola is x = -y²/8 + y/4 - 65/8

5) The end points of the latus rectum are (-10, -3), and (-10, 5)

Step-by-step explanation:

The focus of the parabola = (-10, 1)

The directrix of the parabola, x = -6

The directrix; x = h - p

The focus, F(h + p, k)

Therefore, we have;

h + p = -10

h - p = -6

2·h = -16

h = -8

p = -10 - h = -10 - (-8) = -2

p = -2

Therefore, we have;

1) The vertex of the parabola, (h, k) = (-8, 1)

2) Therefore, the parabola opens left

3) The axis of symmetry is the line y = 1

For P < 0, the equation of the parabola is of the form (y - k)² = 4·p·(x - h)

Therefore, the equation of the parabola is (y - 1)² = 4×(-2)×(x - (-8))

(y - 1)² = 4×(-2)×(x - (-8)) = y² - 2·y + 1 = -8·x - 64

∴ y² - 2·y + 1 + 64 = -8·x

x = -y²/8 + y/4 - 65/8

4) The equation of the parabola is x = -y²/8 + y/4 - 65/8

5) The end points of the latus rectum are (h + p, k + 2·p) and (h + p, k - 2·p)

Therefore, the end points of the latus rectum of the given parabola are;

(-8 + (-2), 1 + 2×(-2)) and (-8 + (-2), 1 - 2×(-2))

(-10, -3), and (-10, 5)


Related Questions

Using the grid below, let's plot the following points and label them with the letter.

A) (2,1)
B) (0,0)
C) (-4,3)
D) (-2,-5)
E) (1,-3)
F) (0,4)
G) (-5,1)
H) (-2,0)

Answers

Answer:

Step-by-step explanation:

A: look at the graph, find the x axis of 2 and on the y axis 1.

B basically the center

C look for x axis of -4, y axis for 3

D x axis -2, y axis -5

E x axis 1, y axis -3

F Center then go up 4

G x axis -5, y axis 1

H x axis -2, y axis 0

All the points A(2, 1), B(0, 0), C(-4, 3), D(-2, -5), E(1, -3), F(0, 4), G(-5, 1), and H (-2, 0) are located on the graph.

What is coordinate geometry?

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

The points are given below.

A(2, 1), B(0, 0), C(-4, 3), D(-2, -5), E(1, -3), F(0, 4), G(-5, 1), and H (-2, 0)

All the points A(2, 1), B(0, 0), C(-4, 3), D(-2, -5), E(1, -3), F(0, 4), G(-5, 1), and H (-2, 0) are located on the graph.

The graph is attached below.

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

#SPJ2

Solve the quadratic equation.
m^2/15 -3 = 2​

Answers

The answer is [tex] 5 \sqrt{3} [/tex]

Explanation :

[tex] \frac{ {m}^{2} }{15} - 3 = 2[/tex]

[tex] \frac{ {m}^{2} }{15} = 2 + 3[/tex]

[tex] \frac{ {m}^{2} }{15} = 5[/tex]

[tex] {m}^{2} = 5 \times 15[/tex]

[tex] {m}^{2} = 75[/tex]

[tex]m = \sqrt{75} [/tex]

[tex]m = \sqrt{25 \times 3} [/tex]

[tex]m = \sqrt{25} \times \sqrt{3} [/tex]

[tex]m = 5 \sqrt{3} [/tex]

CMIIW

I will give
Brainliest

Answers

Answer:

yx=yz+ax

Step-by-step explanation:

find the value of x ​

Answers

Answer:

110°

Step-by-step explanation:

In triangle AOB

OA = OB (radii of same circle)

[tex] m\angle OAB = m\angle OBA =20\degree [/tex]

[tex] m\angle AOB = 180\degree - (20\degree +20\degree) [/tex]

[tex] m\angle AOB = 180\degree - 40\degree [/tex]

[tex] m\angle AOB = 140\degree [/tex]

[tex] m\widehat {ACB} =m\angle AOB = 140\degree[/tex]

(measure of minor arc is equal to corresponding central angle)

[tex] x\degree = \frac{1}{2} (360\degree - 140\degree) [/tex]

(inscribed angle theorem)

[tex] x\degree = \frac{1}{2} \times 220\degree [/tex]

[tex]\huge\purple {x = 110} [/tex]

What is the likelihood of choosing a red pen from the following pack of pens?

A pack of 20 pens contains 5 red pens, 5 blue pens, and 10 black pens.

A.
Impossible

B.
Unlikely

C.
Likely

D.
Certain

Answers

Answer:

unlikely

Step-by-step explanation:

It's unlikely because half of the pens are black and red is only 25% of the total.

Find the values of x and y.

Answers

Answer:

y=180-63-63/2=27degree...in triangle mln

x=180-27-63=90....in triangle mon

Answer:

y=27, x=80

Step-by-step explanation:

∠N= 63°(angles opposite to equal sides)

2∠y+63+63=180°(angle sum property)

2∠y=54°

∠y=27°

27°+63°+∠x=180°(ASP)

∠x=180°-90°=90°

Hope it helps, mark me brainliest pls

Can someone pls help me with this?

Answers

Answer:

the answer is C

Step-by-step explanation:

Give the vertex on the following graph, state whether it is a minimum or maximum?
Answer:
Pls

Answers

Answer:

maximum- (-3,5)

Step-by-step explanation:

52 in
39 in
What is the length of the hypotenuse?
C =
inches

Answers

C, the hypotenuse is 65 in

A wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. Find the speed of the boat as she paddles if the river current is 2 km/h (2 answers)

Answers

Answer:

Step-by-step explanation:

5 km/h or 6 km/h

Step-by-step explanation:

Let the speed of the boat be x

Speed against the current in the river is x - 2

Time in the river:

6/(x - 2)

Time in the lake:

15/x

The difference:

6/(x - 2) = 15/x - 1

Solve for x to find the speed of the boat

Multiply both sides by x(x - 2) to clear the fraction:

6x = 15(x - 2) - x(x - 2)

6x = 15x - 30 - x² + 2x

x² - 11x + 30 = 0

(x - 5)(x - 6) =0

x -5 = 0, x - 6 = 0

x = 5 km/h, x = 6 km/h

Can yalllll plllllssss hellppp meeee

Answers

Ummm .... the answer is D

What is the slope of (-7,-1) (9,-9)

Answers

Answer:

-8/16 or -1/2

Step-by-step explanation:

Hi, use the slope-intercept formula (rise over run)

(y₂-y₁)/(x2-x1)

(-9--1)/(9--7)

(-9+1)/(9+7)

-8/16

-1/2

In 1978, a Japanese designer named Tomoyuki Ono grew the first cube-shaped watermelon.
The fruit is placed in a box when it is small, and it grows into the shape of the box. Akira
bought one of these cube-shaped watermelons at the market. The watermelon's edges were
11 inches long.
What was the volume of Akira's watermelon?
Write your answer as a whole number or decimal. Do not round.

Answers

Volume = length * width * height
Volume = 11*11*11
Volume = 1331 cubic inches

Help! Please!
Factor the polynomial completely.
32z^5-2z

Answers

Answer:

2z(4z^2+1)(2z+1)(2z-1)

Step-by-step explanation:

here is just some basic polynomial factoring where you find something both the numbers have in common and you take that out of the equation. here i just went a little bit deeper and after taking out the common factor i also expanded my answer further as this would be the fully correct answer.

hope this helps!

Answer:

2 z ( 4 z ^2 + 1 )( 2 z+ 1 ) ( 2 z − 1 )

Step-by-step explanation:

Edwin has £300 in his savings account His bank offers him a fixed 5% simple interest rate per annum for a period of 3 years How much internet will he have earned after 3 years?

Answers

Answer: £45

Step-by-step explanation:

First find the amount of simple interest in on year:

= Amount * simple interest rate

= 300 * 5%

= £15

Now that you have the annual interest, the 3 year interest is:

= 15 * 3 years

= £45

What what is this help please

Answers

8 units to the right and 5 units down. I feel so smart right now I’m glad I learned this in middle school :))

c)PLEASE MAN PEOPLE ARE USING ME FOR POINTS
Calculate the measures of spread for Mrs Hampton's class data. Justify your
response by describing the process used to find each measure, (2 points)

Answers

The measures of spread include the range, quartiles and the interquartile range, variance and standard deviation. Let's consider each one by one.

Interquartile Range:

Given the Data -> First Quartile = 2, Third Quartile = 5

Interquartile Range = 5 - 2 = 3

Range: 8 - 1 = 7

Variance:

We start by determining the mean,

[tex]\:1+\:2+\:3+\:3+\:3+\:5+\:8 / 7 = 3.57[/tex]

n = number of numbers in the set

Solving for the sum of squares is a long process, so I will skip over that portion and go right into solving for the variance.

[tex]\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1},\\\\=> SS/n - 1\\\\=> 31.714/7 - 1\\=> 5.28571[/tex]

5.3

Standard Deviation

We take the square root of the variance,

[tex]\sqrt{5.28571} = 2.29906[/tex]

2.3

If you are not familiar with variance and standard deviation, just leave it.

Answer:

the one above is right lol

Step-by-step explanation:

Solve the system of equations by the addition method.
9x + y = - 12
8x - y = 5

Answers

Step-by-step explanation:

9x + y = -12

8x -y = 5

17X = -7

x -7/17

8(-7/17) -y = 5

-3.3 - Y = 5

-y = 8.3

Y = -8.3

What operation does the expression "7y" mean?

Answers

Answer:

Multiplication

Step-by-step explanation:

7y means 7 times the value of y. So 7 times y = 7y

I NEED HELP ASAP!!! Question is in the photo

Answers

Answer:

x = 88.333

Step-by-step explanation:

Octagon = 1080 degrees

1080 = 2x + x + 143 + 152 + 116 + 125 + 140 + 139 (Clean up the problem)

1080 - 815 = 3x

265 = 3x (Divide each side by 3)

x = 88.333

54 out of the 90 employees at the water slides are temporary employees. What percentage of the employees at the water slides are temporary?

I need help ASAP PLEASE!!!!

Answers

54/90= 0.6 * 100%= 60%
The answer is 60%

If, on their own, it takes 6 hours for Person A to complete a task and 9 hours for Person B to complete the same task, then how many hours would it take if they worked together? Estimate your answer to 4 places after the decimal, if necessary.

Answers

Answer:

Step-by-step explanation:

A does 1/6 of the task per hour.

B does 1/9 of the task per hour.

Together, they do 1/6+1/9 = 5/18 of the task per hour, finishing in 18/5 hours.

18/5 = 3.6 hours

Determine whether the given value is a solution of the equation.
b
6; b =78
13
78 (select) a solution.

is 78 the solution or not

Answers

Answer:

78 is a solution

Step-by-step explanation:

The given equation is b/13 = 6

Therefore, by applying the multiplication property of equality, we have by multiplying both sides by 13, we have;

b/13 × 13 = 6 × 13

The 13 in the denominator of b/13 divides the 13 in the multiplicand to give 1, and we get the following equation

b/13 × 13 = b × 1

Therefore;

b/13 × 13 = b × 1  = 6 × 13 = 78

b × 1 = 78

By the multiplicative identity property of '1', we get;

b × 1 = 1 × b = b

∴ b × 1 = b = 78

b = 78

∴ 78 is a solution of the equation.

Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6.

Answers

Step-by-step explanation:

When lines are perpendicular to each other

multiplying their gradients(m) will equal to - 1

so , m1 × m2 = -1

1st:Find m1

5x+6y= -6

make y the subject,

6y= -5x -6

[tex]y = \frac{ - 5x - 6}{6} [/tex]

y= -5/6x - 1

because y = mx + c

m1 = -5/6

2nd:find m2

-5/6 × m2 = -1

m2 = 6/5

3rd: substitute m2 and the coordinates into y=mx+c

y=mx+c

-1= (6/5)(-2)+c

-1 = -12/5 + c

-5 = -12 + c

-5+12= c

c = 7

4th: substitute m2 and c into y= mx+c to find the equation the line

y =6/5x + 7 (Ans)

As per slope-intercept form, the equation of the line through point (−2,−1) and perpendicular to 5x + 6y = -6 is 5y = 6x + 7.

What is the slope-intercept form of a straight line?

The slope-intercept form of a straight line is y = mx + c.

Here, 'm' is the slope and 'c' ix the y-intercept of the given line.

The given equation is 5x + 6y = - 6

Therefore, in slope-intercept form, this equation will be:

y = - 5x/6 - 1

Therefore, the slope of this line is m = - 5/6 and the y-intercept is c = - 1.

The required line is perpendicular to the given line.

Therefore, the slope of the required line is

= - 1/m

= 6/5

Again, the required line passes through the point (- 2, - 1).

Therefore, - 1 = - 2(6/5) + c

⇒ c = - 1 + 12/5

⇒ c = 7/5

The equation of the required line is

y = (6/5)x + 7/5

⇒ 5y = 6x + 7

Learn more  about the slope-intercept form of a straight line here: https://brainly.com/question/14534555

#SPJ3

Find the equation of the line shown

Answers

Answer:

y=2x

Step-by-step explanation:

as y goes up 2 x goes up 1

Y=2x because if you make t table you’ll see the slope is 2 and the line begins at 0 so the y intercept is 0

Mary, Rachel, and Tommy went out for lunch. Mary
spend half of what Tommy spent. Rachel spend $12
less than what Tommy spent. Mary spent $8.50.
a) How much did Tommy spend? Explain how you got
your answer.

HELP
I got that they all spent 44.50 but I’m not sure...

Answers

Answer:

Tommy spent $17

Step-by-step explanation:

Mary spent half of what tommy spent. 8.50 x 2= 17

therefore tommy spent $17

Answer:

tommy spent $17

Step-by-step explanation:

8.50 X 2 is 17 and if Rachel spent $12 less than tommy did Rachel spent $5.

In total they spent $30.50

Wich value of x is a solution of 5 x + 13 _ = _____ ? x 6

Answers

Answer:

ANSWER IS x = 2.6

[tex]5x + 13 = \: 2.6\times 6[/tex]

Step-by-step explanation:

[tex]5x + 13 \\ x = 13 \div 5 \\ x = 2.6[/tex]

A certain tree can grow 0.445 meter in one year. At
that rate how much can the true grow in 3 years?

Answers

Answer:

1.335

Step-by-step explanation:

you have to do this equation .445 x 3 =1.335

Mai has $36 to spent on movie tickets. Each ticket cost $4.50. How many tickets can she buy?

Answers

Answer:

8 tickets

Step-by-step explanation:

To find how many she can buy, divide 36 by 4.5

36/4.5

= 8

So, Mai can buy 8 movie tickets

Latoya is building a fence around her garden. For every 4 feet of fencing, the cost is $36.

Answers

Answer:

Length of fencing: 4, 6, 7, 9, 10

Cost: 36, 54, 63, 81, 90

Step-by-step explanation: I hope this gave you your answer!!

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