A parabola can be drawn given a focus of (4, -3) and a directrix of x=2 Write the equation of the parabola in any form​

Answers

Answer 1

Answer:

The equation of the parabola  ( y +3)² = 4 ( x-3)

Step-by-step explanation:

Step(i):-

we know that the focus of the parabola (h + a , k ) and directrix is   x = h - a

Given

 focus of the parabola (h + a , k ) = ( 4, -3 )

  Equating                h + a =4 ..(i)

                              and k =-3

Given directrix is   x = 2

                          h - a =2 ..(ii)

Adding (i) and (ii) equations , we get

                   h + a + h-a = 4+2

                      2 h = 6

                         h =3

   substitute h=3 in equation (i)

                h + a =4

               3 + a =4

                  a = 1

The length of Latus rectum 4a = 4(1) =4

Step(ii):-

The vertex ( h, k) = ( 3 , -3) and a = 1>0

Given directrix is x = h - a = 2 so the parabola axis is lie on X- axis and symmetric about x-axis

The equation of the parabola

( y - k )² = 4 a ( x - h )

( y - (-3))²= 4(1) ( x - 3 )

The equation of the parabola  ( y +3)² = 4 ( x-3)

                             


Related Questions

What is the approximate value of sin C?
B
13.93
5
A
13
12
O A. 0.93
OB. 0.36
O C. 2.79
D. 0.38

Answers

Answer: 0.36

Step-by-step explanation:

Ap3x

What does x equal I this problem

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Answer: The answer is X= 9    Hope this helps :)  Please mark Brainliest

Step-by-step explanation:

Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1,670 km per hour. What is the circumference of Earth's equator?

Answers

Answer:

Solution in photo

Step-by-step explanation:

Mrs. Maxwell is teaching a 5th grade class. She is standing 9 meters in front of Bruce. Ruth is sitting to Bruce's right. If Ruth and Mrs. Maxwell are 15 meters apart, how far apart are Bruce and Ruth?

Answers

9514 1404 393

Answer:

  12 m

Step-by-step explanation:

The distances of interest are the sides of a right triangle whose right angle is at Bruce. The hypotenuse of the triangle is the Teacher-Ruth distance. The unknown side (x) can be found using the Pythagorean theorem:

  x² + 9² = 15²

  x² = 225 -81 = 144

  x = √144 = 12

Bruce and Ruth are 12 meters apart.

In football A field goal counts three points and extra point after touchdowns Count as one point a kicker score 30 points on 16 kicks how many of the Kicks are field goals

Answers

Answer:

2

Step-by-step explanation:

3x30=90

15x3=45

90/45=2

Answer:

He makes 14 field goals and 7 extra point kicks

Step-by-step explanation:

f=#of field goals

e=extra kick points

f+e=21

3f+1e=49

subtract top from bottom

2f=28

f=14

Good luck!

I need help thank you.

Answers

Answer:

x ≤ 1

Step-by-step explanation:

The graph goes in the left direction, meaning the inequality needs to be less than.

The point is at the point positive 1 and has a shaded dot, meaning the inequality needs to be less than or equal to 1.

Answer:

B

Step-by-step explanation:

x ≤ 1

As thee circle at 1 is filled,you have to include 1 also

simplify the expression 3 √ 2 - 5 √ 18​

Answers

−12√2
(mark brainliest if correct plss)

I need to know this ASAP please! What is 2/3x + 1/3x?

Answers

Answer:

x

Step-by-step explanation:

2/3x+1/3x=x

Answer:

1

Step-by-step explanation:

2/3x + 1/3x

2+1/3x

3/3x

=x

one x value is 1

Find the slope of the line.
-1
3
-10
-11
12
4
3
2 0 1
9 10
The slope is
Turn

Answers

-1

Step-by-step explanation:

because looking at the graph it is negative, and it goes down one over one

plzzzzzzzzzzzzzzzzzzzzzzz

Answers

Option C. Please mark me as brainliest.

Plz answer this!⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️

Answers

Answer:

1/2 ÷ 3/10

1/2×10/3

5/3

1 2/3

1) option is correct

9514 1404 393

Answer:

  1)  1 2/3

Step-by-step explanation:

The model of choice 1 shows that 3/10 goes into 1/2 one and two-thirds times. That also happens to be the only model with the correct result.

  1/2 ÷ 3/10 = 5/10 ÷ 3/10 = 5/3 = 1 2/3

A toddler section of a pool mesures 7 feet by 8 feet. What is area of the toddler section

Answers

Answer:

56 ft^2

Step-by-step explanation:

Question 7 of 25 Which of the binomials below is a factor of this trinomial? x - 6x-16 O A. X-1 O B. X-8 OC. X-16 O D. x-2​

Answers

Answer:

(x-8) is the factor.

Step-by-step explanation:

The given trinomial is [tex]x^{2}-6x-16[/tex].

We need to find the factor of this trinomial.

[tex]x^{2}-6x-16=x^2-8x+2x-16\\\\=x(x-8)+2(x-8)\\\\=(x+2)(x-8)[/tex]

The factors of [tex]x^{2}-6x-16[/tex] is (x-2) and (x-8).

So, the factor of [tex]x^{2}-6x-16[/tex] is (x-8). Hence, the correct option is (B).

in the recent year, 51.9 billion cans were recycled. About how many cans per this week

Answers

998076923.077 per week

What is 70% of 40??????

Answers

Answer:

28

Step-by-step explanation:

hope this helps

Answer:

28

Step-by-step explanation:

70% is equal to 70/100. "of" when used in math means multiplaication.

so we do 70/100 x 40

we can simplify 70/100 to get 7/10.

now we multiply:

7/10 x 40 = 28

solve for y when x=4

-y+5x=2(y+7x)

A. y=18
B. y=7
C. y=4
D. y=-12

Answers

Answer:

D.) y=-12

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!! :)

Can someone help me with letter D?

Answers

Answer:

1.5 times greater because the ratio of triangle ABC to triangle DEF is 2:3

Step-by-step explanation:

Answer:

1.4 times is the correct answer

1/6x + 3/2 slope of line

Answers

Answer: m=1/6

Step-by-step explanation:

The graph below represents one function, and the table represents a different function. How are the functions similar? How are they different?

Answers

Answer:

Step-by-step explanation:

they both go thur the point (0,-4)  so they both have the same b in the slope intercept from  of  y =mx +b

but.. they have a different slope... m , the graph has a slope m of 4/3 while the table has a slope of 1  , both positive.. :)

The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

From the graph, using the point (3, 0) and (0, -4):

y - 0 = [(-4 - 0)/ (0 - 3)](x - 3)

y = (4/3)x - 4

From the table using (0, -4) and (2, -2):

y - (-4) = [(-2-(-4))/(2-0)](x - 0)

y = x - 4

The equation given by the graph is y = (4/3)x - 4 while the table is y = x - 4. Both equation have a y intercept of -4.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ2

I need help with this please

Answers

Answer:

b

Step-by-step explanation:

there's a property for Alternate Interior Angles

Answer:

Choice B

Step-by-step explanation:

The reason why < 3 is equal to < 6 is because they are alternate interior angles.

The first choice are supplementary angles they add up to 180 so they can't be equal.

The third one is false because we don't actually know the measurements of the angles but they both need to be 45° to add up to 90 since they are equal to each other.

The last one is also incorrect because they are vertical angles just like the third choice and they aren't on a line so they can't add up to 180.

ASAP can someone help and explain this to me

Answers

Answer:

[tex]d = 15.0[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra II

Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Step-by-step explanation:

Step 1: Define

Point C (7, -4)

Point D (-8, -5)

Step 2: Find distance d

Substitute [DF]:                    [tex]d = \sqrt{(-8-7)^2+(-5+4)^2}[/tex]Subtract/Add:                       [tex]d = \sqrt{(-15)^2+(-1)^2}[/tex]Exponents:                           [tex]d = \sqrt{225+1}[/tex]Add:                                      [tex]d = \sqrt{226}[/tex]Evaluate:                              [tex]d = 15.0333[/tex]Round:                                 [tex]d = 15.0[/tex]

pls help meeeeeeeeee

Answers

1. C 2.E 3.A 4.F 5.D 6.B
Question 2- 1.< 2.< 3.>= 4.< 5.>= 6.>

What is the exact value of tan ( 5 pi/8 )

Answers

Answer: Choice D) [tex]\tan\left(\frac{5\pi}{8}\right) = - \sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]

===================================================

Explanation:

Make sure your calculator is in radian mode. Use your calculator to find that tan(5pi/8) = -2.41421 which is approximate.

Since the value is negative, this means the answer is between choices C and D. You can use your calculator to compute those expressions given and you should find it matches with choice D.

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

Further explanation:

We can apply the half angle identity for tangent like so

[tex]\tan\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\\\\\\\tan\left(\frac{5\pi/4}{2}\right) = -\sqrt{\frac{1-\cos(5\pi/4)}{1+\cos(5\pi/4)}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1-\left(-\frac{\sqrt{2}}{2}\right)}{1+\left(-\frac{\sqrt{2}}{2}\right)}}\\\\\\[/tex]

Simplifying further, we get

[tex]\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]

In the last step, I multiplied top and bottom of the outer fraction by 2 to clear out the denominators of the inner fractions.

Answer:

Answer D

Step-by-step explanation:

on edge 2023

Please help me! Thank you so much!

Answers

Answer: It's (A) 12<X

Step-by-step explanation: I chose that one because the line highlighted on the number line, it's bigger than 12!

I need that r d d d d d. D d d d d d d. D

Answers

Answer:

D is not a function.

Step-by-step explanation:

The first option is a function because it makes up a straight line.  The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function.  The third option is also a function because there is no more than one point for each x value.  The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.

Answer:

D is not a function.

Step-by-step explanation:

The first option is a function because it makes up a straight line.  The second option is also a function because it is also known as y = -3/2x + 2 creating a slope function.  The third option is also a function because there is no more than one point for each x value.  The last option is not a function because the number 2 is going for 2 variables A and B and you can't have them with more than one so D is your answer.

this months rainfall is 30% less than last months total of 3.5 inches.

PLZZZZ ANSWWERRR ASAPPP MARKING BRAINLIEST

Answers

Answer:

1.05

Step-by-step explanation:

3.5x.30=1.05

Answer:

1.05

Step-by-step explanation:

You will have to multiply if you are trying to find the amount of water in total. So, 0.30*3.5=1.05. So, that would be your answer for the amount of rainfall.

PLEASE HELP ASSP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

0.96% or 1% to the nearest whole ( use the whole as for your answer )

Step-by-step explanation:

825-817 = 8

8 / 825 = 0.00969696....

x 100 = 0.96%

what is the answer to the question?​

Answers

Answer:

120°

Step-by-step explanation:

m<ABD+m<DBC=m<ABC

61°+59°=120°

hope this helped!

Answer:

We conclude that the value of m∠ABC = 120°

Step-by-step explanation:

Given

m∠ABD = 61°

m ∠DBC = 59°

To Determine

m∠ABC = ?

It is clear that the value of m∠ABC can be determined by adding m∠ABD and m∠DBC because m∠ABC the segment BD divides the angle m∠ABC into two adjacent angles m∠ABD and ∠DBC.

Therefore,

m∠ABC = m∠ABD + m∠DBC

             = 61° + 59°            ∵ m∠ABD = 61°, m ∠DBC = 59°

             = 120°

Therefore, we conclude that the value of m∠ABC = 120°

in an 7th grade class with 80 people, seven tenths of the students wore shorts, how many students wore shorts

Answers

Answer:

56

Step-by-step explanation:

80 x (7 / 10) = 56

80 times 7=560

560/10=56

Answer: 56

Can someone help me please

Answers

Answer: B

Step-by-step explanation:

It has to be B. None of the other answers make sense.

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