1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sineoko [7]
3 years ago
10

What is the equation of the parabola with focus (3, 0) and directrix x = –3?

Mathematics
2 answers:
butalik [34]3 years ago
8 0

Answer:

y²-12x = 0

Step-by-step explanation:

The formula for calculating the equation of a parabola is y² = 4ax

and x = a

To find the equation of the parabola with focus (3, 0) and directrix x = –3,

The point given (x,y) = (3,0) and x = -3

From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3

Similarly, x = 3 from the given point.

Substituting the value of x = -3 in the formula for equation of a parabola gives;

y² = 4(-3)x

y²= -12x

y²-12x = 0

nikitadnepr [17]3 years ago
4 0

Answer:

x = \frac{1}{12} y²

Step-by-step explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

\sqrt{(x-3)^2+(y-0)^2} = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x = \frac{1}{12} y²

You might be interested in
1/6+1/2 simplest form
vlada-n [284]
Lowest common denominator-> 6
1/2 multiply both top and bottom by 3 to get it in sixths
1/6+3/6=4/6
4/6 simplifies to 2/3.
2/3 is the simplest form to your question.
7 0
3 years ago
Plz help
frozen [14]

Answer:

a. Required system of equations is:

c+p = 10

5c+4p = 46

b. 6 cakes were sold

Step-by-step explanation:

Let p be the number of pies and c be the number of cakes.

Then according to given statement " the store sold 10 baked goods"

c+p = 10\ \ \ Eqn\ 1

And

"A cake costs $5 and a pie costs $4"

5c+4p = 46\ \ \ \ Eqn\ 2

Using equation 1,

c=10-p

Putting this value of c in equation 2:

5(10-p)+4p = 46\\50-5p+4p = 46\\-p = 46-50\\-p = -4\\p = 4

Putting p = 4 in equation 1

c+4 = 10\\c = 10-4\\c =6

Hence,

a. Required system of equations is:

c+p = 10

5c+4p = 46

b. 6 cakes were sold

7 0
3 years ago
A rectangle has a perimeter of 18 cm.its length is 5 cm greater than its width.find the dimensions.
Marat540 [252]
P=18
l=5 cm greater than the width
w=5 less than the length

USE YOUR NUMBER SENSE!!! - just plug in different number below 4 to figure out the width

3=w  3+5=8 8+8=16+6=22    WILL NOT WORK

2=w   2+5=7  7+7=14   14+2+2= 18    WE HAVE A WINNER!!!!

FInal Answer: width: 2 cm and length: 7 cm
                          


5 0
3 years ago
Add [1/-4 3/5] [-2/6 -2/4]
brilliants [131]

Answer:

​25/138

Step-by-step explanation:

1 Convert 4\frac{3}{5}4

​5

​

​3

​​  to improper fraction. Use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

​c

​

​b

​​ =

​c

​

​ac+b

​​ .

\frac{1}{-(\frac{4\times 5+3}{5})}(-\frac{2}{6}-\frac{2}{4})

​−(

​5

​

​4×5+3

​​ )

​

​1

​​ (−

​6

​

​2

​​ −

​4

​

​2

​​ )

2 Simplify  4\times 54×5  to  2020.

\frac{1}{-(\frac{20+3}{5})}(-\frac{2}{6}-\frac{2}{4})

​−(

​5

​

​20+3

​​ )

​

​1

​​ (−

​6

​

​2

​​ −

​4

​

​2

​​ )

3 Simplify  20+320+3  to  2323.

\frac{1}{-(\frac{23}{5})}(-\frac{2}{6}-\frac{2}{4})

​−(

​5

​

​23

​​ )

​

​1

​​ (−

​6

​

​2

​​ −

​4

​

​2

​​ )

4 Simplify  \frac{2}{6}

​6

​

​2

​​   to  \frac{1}{3}

​3

​

​1

​​ .

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{2}{4})

​−(

​5

​

​23

​​ )

​

​1

​​ (−

​3

​

​1

​​ −

​4

​

​2

​​ )

5 Simplify  \frac{2}{4}

​4

​

​2

​​   to  \frac{1}{2}

​2

​

​1

​​ .

\frac{1}{-(\frac{23}{5})}(-\frac{1}{3}-\frac{1}{2})

​−(

​5

​

​23

​​ )

​

​1

​​ (−

​3

​

​1

​​ −

​2

​

​1

​​ )

6 Find the Least Common Denominator (LCD) of \frac{1}{3},\frac{1}{2}

​3

​

​1

​​ ,

​2

​

​1

​​ . In other words, find the Least Common Multiple (LCM) of 3,23,2.

LCD = 66

7 Make the denominators the same as the LCD.

-\frac{1\times 2}{3\times 2}-\frac{1\times 3}{2\times 3}−

​3×2

​

​1×2

​​ −

​2×3

​

​1×3

​​

8 Simplify. Denominators are now the same.

-\frac{2}{6}-\frac{3}{6}−

​6

​

​2

​​ −

​6

​

​3

​​

9 Join the denominators.

\frac{-2-3}{6}

​6

​

​−2−3

​​

10 Simplify  -\frac{1}{3}-\frac{1}{2}−

​3

​

​1

​​ −

​2

​

​1

​​   to  -\frac{5}{6}−

​6

​

​5

​​ .

\frac{1}{-(\frac{23}{5})}\times \frac{-5}{6}

​−(

​5

​

​23

​​ )

​

​1

​​ ×

​6

​

​−5

​​

11 Move the negative sign to the left.

-\frac{1}{\frac{23}{5}}\times \frac{-5}{6}−

​

​5

​

​23

​​

​

​1

​​ ×

​6

​

​−5

​​

12 Invert and multiply.

-\frac{5}{23}\times \frac{-5}{6}−

​23

​

​5

​​ ×

​6

​

​−5

​​

13 Use this rule: \frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}

​b

​

​a

​​ ×

​d

​

​c

​​ =

​bd

​

​ac

​​ .

-\frac{5\times -5}{23\times 6}−

​23×6

​

​5×−5

​​

14 Simplify  5\times -55×−5  to  -25−25.

-\frac{-25}{23\times 6}−

​23×6

​

​−25

​​

15 Simplify  23\times 623×6  to  138138.

-\frac{-25}{138}−

​138

​

​−25

​​

16 Move the negative sign to the left.

-(-\frac{25}{138})−(−

​138

​

​25

​​ )

17 Remove parentheses.

\frac{25}{138}

​138

​

​25

​​

7 0
3 years ago
A recent study of 200 nurses found that of 125 female nurses, 56 had bachelor's degrees; and of 75
Natasha_Volkova [10]
For the answer to the question above asking about probabilities.
<span>the answer for a) would be 56/200 = 7/25
The answer for  
b) would be 75/200 = 3/8 and
lastly the answer for
c)34/200 = 17/100
</span>I hope my answer helped you. Feel free to ask more questions. Have a nice day!
6 0
3 years ago
Read 2 more answers
Other questions:
  • If i wanted to find out how much fencing i would need to buy for my rectangle yard i could.
    5·1 answer
  • How to solve this math -9(-6w+3u-4)
    9·1 answer
  • How do I do this I'm working on as fractions please help me please please please
    8·2 answers
  • 2^x = 1/2<br><br> A:-1<br> B:-1/2<br> C:1
    13·1 answer
  • PLS HELP ASAP
    13·1 answer
  • How many times as great is 9 x 10⁵ as 3 x 10⁵
    5·1 answer
  • Sarah and 9 of her friends went to the movies. They each bought the popcorn, soda and Twizzlers. The popcorn was $6.25, the soda
    13·2 answers
  • If it says product what does it mean? Does it mean addition subtraction equals division or multiplication?
    9·2 answers
  • 2/3 (12x-9) i need help on this
    15·2 answers
  • Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection. Which function f represents
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!