What is the equation of the parabola, in vertex form, with focus at (2,-4) and directrix y=-6?

A. (X-2)^2 = 4(y+5)
B. (Y+4)^2 = 4(x-2)
C. (X+2)^2 = 1/4(y+4)
D. (X-2)^2 = -1/4(y+5)

What Is The Equation Of The Parabola, In Vertex Form, With Focus At (2,-4) And Directrix Y=-6?A. (X-2)^2

Answers

Answer 1

Answer:

A. (X-2)^2 = 4(y+5)

Step-by-step explanation:

Answer 2

Equation of parabola: (x-2)² = 4(y+5)

Thus option A is correct.

Given:

Focus at (2, -4) and a Directrix of y = -6

Here,

Let us suppose that there is a point (x, y) on the parabola.

Its distance from the focus point (2, 4) is √(x - 2)² + (y + 4)²

Its distance from directrix y = -6 is |y + 6|

Therefore, the equation will be:

√(x - 2)² + (y + 4)² = |y + 6|

Squaring on both the sides,

(x - 2)² + (y + 4)² = (y + 6)²

x² - 4x + 4 + y² + 8y + 16 = y² + 12y + 36

(x-2)² = 4(y+5)

Therefore option A is correct.

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Related Questions

4 2/3 divided by 1/2 in fraction form

Answers

Answer:

9 1/3

Step-by-step explanation:

4 2/3 = 14/3

14/3/1/2

14/3 x 2/1

28/3= 9 1/3

help!!!!!!!!!!!!!!!!! due in 15min

Answers

Answer:

5

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

When you put the i out in place for x you multiply so

4x9=36

7x9=63

2x9=18

9x9=81

Please answer quick!!! Will Mark BRAINLIEST!!!

Answers

Answer:

picture 1 : 360 cm2

picture 2:  sorry I don't really know

picture 3: 11.25 cm2

Step-by-step explanation:

hope this helps

HELP!!! I do not understand!

Answers

y= -4/7x + 5 is parallel

After selecting 180 of its employees to from a new division, a company discovers that engineers outnumber analysts by a 3:1 ratio in the division. Oly analysts and engineers work in the new division. How many more analysts must the company add to the division if it wants to have a 1:1 ratio of engineers to analysts at the new division?

Answers

Answer:

I think its 90

Step-by-step explanation:

3x plus 1x is 4x divide 180 but 4 and get 45 so that meab there are 135 and 45

you need 90 more analysts to have a 1 to 1 ratio

The formula: y-y1 = m (x-x1) is known as:​

Answers

Answer:

point slope form.

Step-by-step explanation:

this is different from slope intercept form. use these when dealing with cartesian graphs using slope and points along x, y

please please help me

Answers

Answer:

-0.88

Step-by-step explanation:

(f/g)(9)=(x+7)/-2x and the 9 brackets is the value of x with which you have to substitute. after u do that you get (9+7)/-18=16/-18=-0.88(8)

Drag the numbers to create three ratios that are equivalent to 4:12.
Numbers can only be used once.

Pls help

Answers

first blank is 60 second blank is 12 third blank is 2

A scale drawing for a backyard is shown below.
In the drawing, 2 cm represents 5 m.
Assuming the patio is rectangular, find the area of the real patio.

Answers

Answer:

50 m²

Step-by-step explanation:

2 cm for length = 5 m. 4 cm for width = 10 m. Area = width • length. 10•5=50

the product of two number is 20 and the sum of square is 41 find the number​

Answers

Answer:

Answer. The numbers are 4 and 5. Their sum = 25 + 16 = 41.

Rationalize the denominator and simplify 6/√2-√3

Answers

Answer:

Step-by-step explanation:

[tex]\frac{6}{\sqrt{2} - \sqrt{3} } * \frac{\sqrt{2} + \sqrt{3} }{\sqrt{2} + \sqrt{3} }[/tex]

[tex]\frac{6\sqrt{2} + 6\sqrt{3} }{2-3}[/tex]

[tex]-6(\sqrt{2} + \sqrt{3} )[/tex]

The fraction after rationalizing the denominator is given by the equation

A = -6 ( √2 + √3 )

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = 6 / ( √2 - √ 3 )   be equation (1)

Now , on simplifying the equation , we get

To rationalize the denominator of the fraction ,

Multiply the denominator by its conjugate ,

So , the conjugate of ( √2 - √ 3 ) = ( √2 + √ 3 )

Multiplying the numerator and denominator of the fraction by ( √2 + √ 3 )

A x ( √2 + √ 3 ) / ( √2 + √ 3 )

Substituting the values in the equation , we get

[ 6 / ( √2 - √ 3 ) ] x ( √2 + √ 3 ) / ( √2 + √ 3 )

On simplifying the equation , we get

6 ( √2 + √ 3 ) / ( 2² - 3² )

So , the value of A is A = 6 ( √2 + √ 3 ) / ( -1 )

A = -6 ( √2 + √ 3 )

Therefore , the value of A is A = -6 ( √2 + √ 3 )

Hence , the equation A = -6 ( √2 + √ 3 )

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WILL MARK BRAINLIEST ANSWER ASAP
Which answer choice correctly represents an algebraic expression for 8 less than a number?
a. x-8
b. 8-x
c. x+8
d. 8x

Answers

Answer:

A

Step-by-step explanation:

1

1 " a number x" →x.

2

2 "less than a number x" means to subtract →x−

3

3 "8 less than a number x" means to subtract →x−8.

Give each a sum or difference:
a. -12+4=
b. -4+1=
c. 4 - 12=
d. 4+12=

Answers

A. -8
B. -3
C. -8
D. 16

A way to remember corresponding angles is to remember: *

Answers

Haha ahaha hah ahaha haha

Which system of equations is represented by the graph?
10
8
(4.0)
-10-8
-6 -4 -2
8
1D
(-1,-571
y = x +4
X+4
y =
X+2
y = x - 4
X+4
y =
X+2
y = x + 4
X-4
y =
X+2
y = x - 4
X-4
y =
X+2

Answers

Answer:

-6

Step-by-step explanation:

is it

A​ dig-your-own potato farm charges​ $1.27 per pound of potatoes plus​ $0.20 per pound to clean the potatoes. Kevin digs 30 pounds of potatoes. The farm cleans 8 pounds for him. How much does Kevin pay in​ all?

Answers

Answer: $39.70

Explanation:

1.27 x 30 = 38.1

0.20 x 8 = 1.6

38.1 + 1.6 = 39.7

The total number of seats in an auditorium is modeled by the function
f(x) = 2x2 - 6x, where x represents the number of rows of seats.

How many rows are there in the auditorium if it has a total of 416 seats?

Answers

There are 16 rows in the auditorium

given the function f(x)=x^3 +x^2-2x+1 what is the resulting function f(x) is shifted to the left one unit

Answers

Answer:

The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]

Step-by-step explanation:

Suppose we have a function f(x). If we want to shift the function 1 unit to the left, we find f(x+1).

In this question, we have:

[tex]f(x) = x^3 + x^2 - 2x + 1[/tex]

Shifting 1 unit to the left:

[tex]f(x+1) = (x+1)^3 + (x+1)^2 - 2(x+1) + 1[/tex]

[tex]f(x+1) = (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2x - 2 + 1[/tex]

[tex]f(x+1) = x^3 + (3+1)x^2 + (3+2-2)x + 1 + 1 - 2 + 1[/tex]

[tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]

The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]

Can someone do b and c for me please 10 points!!

Answers

Given, a=-3

a) 2a= 2 × -3 = -6

b) a^2= (-3)^2= 9

c) 3a^2= 3 × (-3)^2 = 3 × 9 = 27

Hope it helps uh.

first you do multiply both the a because a is in square then a x a so (-3 x-3) =6 answer is 6

then next is c

3a sq OK

3a sq = (3x-3) -3 x-3

answer is 81

help me.... this is do in 13 min

Answers

Answer:

d

Step-by-step explanation:

The answer would be 2/9

A rectangle has an area of 82 ft2. What is
the length if the width is 10 ft?

Answers

Answer:

187

Step-by-step explanation:

The expression 120 + 15m gives the volume of water in Miguel's pool (in liters) after he spends m minutes filling his pool.

What is the volume of water in Miguel's pool after he fills it for 6.5 minutes?

Answers

Answer:

217.5 liters

Step-by-step explanation:

15 x 6.5 = 97.5. 97.5 + 120 = 217.5 liters

Help me out on this question

Answers

Answer:

3

Step-by-step explanation:

n = (30-12) ÷ 6

n = 18 ÷ 6

n = 3

Answer:

the 1st answer is right

Step-by-step explanation:


Tom walks 1/3
of a mile in 1/4 of an hour. At this rate, how many miles will Tom Walk
in 1 hour?
-
B
IN

Answers

Answer:

4/3 miles

Step-by-step explanation:

1/3 miles

-----------------

1/4 hour

1/3 ÷ 1/4

Copy dot flip

1/3 * 4/1

4/3 miles per hour

In 1 hour

4/3 miles

Answer:

1 1/3 miles in 1 hour

Step-by-step explanation:

since there are 4 quarters in 1, you must multiply 1/3 by 4.

1/3 x 4 = 1 1/3

Solve for x round to one decimal place.

Answers

Answer:

i wanna say 12 but i am not sure!!!!!!!!!

Step-by-step explanation:

Lauren owns 28 acres of land which she rents to a rancher for $3603 per acre per year. Her property taxes are $942 per acre per year. How much profit does she make on the land each​ year?
a) $99,942
b) $127,260
c) $101,826
d) $74,508

Answers

Answer:

B)$127,260

Step-by-step explanation:

28 x 3603= 100884

942 x 28=26376

100884 + 26376= B) $127260

Which is not a method used for changing the attitude of Employee
= Performance appraisal

Answers

Step-by-step explanation:

Performance appraisal is the answer

simplify the expression (-6i)(-6i)​

Answers

Answer:

36i^2 i think that's right

pls help!!!! i will give brainly!!!!
Two quantities are related, as shown in the table:

x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship? (4 points)

y = 1 over 2x + 2
y = 1 over 2x + 1
y = x + 2
y = 2x + 1

Answers

9514 1404 393

Answer:

  (a)  y = 1/2x + 2

Step-by-step explanation:

The only equation that matches the first table entry is ...

  y = 1/2x +2

  3 = (1/2)(2) +2 . . . . first table entry

WORTH 67 POINTS!! PLEASE HELP QUICK!!


A.
B.
C.
D.

Answers

Step-by-step explanation:

When m > -3.1, the line should extend towards the right and the point at 3.1 should be an empty circle. (as m = 3.1 is not included in the solution set)

Hence the answer is Option D.

P.S. The reason why A is wrong is because the number line is wrongly labelled. -3.3, -3.2 and -3.1 are all less than -3 and should be on the left of the number line.

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