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
Verizon [17]
2 years ago
12

Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?

Mathematics
1 answer:
kramer2 years ago
3 0

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3.  Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient.  That narrows the possible answers to A and C.

The x component of the focus is x = 5.  Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations.  The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix.  So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

You might be interested in
A bracelet is exactly 6.97 cm across from one side to the other, through the center. What is the approximate area of the bracele
Vadim26 [7]

Answer:

≈ 38.14 cm²

Step-by-step explanation:

Diameter of circle= 6.97 cm

Area of circle = ?

  • Area = πr² = πd²/4 =
  • 3.14*(6.97)²/4 ≈ 38.14 cm²
3 0
3 years ago
94÷4≈
Tanya [424]

Answer:

ok, te ayudaré

94÷4=23.5

535÷5=107

76÷3=25.33333333333

829÷4=207.25

26÷9=2.8888888889

569÷8=71.125

97÷9=10.7777777778

527÷3=175.6666666667

25÷4=6.25

534÷9=59.3333333333

58÷6=9.6666666667

37÷5=7.4

49÷2=24.5

156÷6=26

I hope it serves you, give me a crown please

7 0
2 years ago
A store has a 25\%25% off sale on coats. With this discount, the price of one coat is \$34.50$34.50. What is the original price
timama [110]

Answer:

$46

Step-by-step explanation:

A percent is a portion of 100. If  we receive 25% off then we pay 75% of the price. 100%-25%=75%. $34.50 is 75% of the original price. We find the new price through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities. For example, we will compare percent over percent to an equal ratio of $ to $.

\frac{75}{100} =\frac{34.50}{y}

I can now cross-multiply by multiplying numerator and denominator from each ratio.

75y=100(34.50)\\75y=3450

I now solve for y by dividing by 75.

\frac{75y}{75} =\frac{3450}{75} \\y= 46....

The original price was $46.


5 0
3 years ago
Enter the correct unit of measurement to complete the conversion. 100 liters = 1 what?
Elanso [62]
<span>10 milliliters (ml) =1 centiliter (cl)1 milliliter =1 cubic centimeter1 liter =1000 cubic centimeters100 centiliter =1 liter (L) = 1,000 milliliters<span>1000 liters =<span>1 kiloliter (km)
</span></span></span>
            
             cubic decimeter<span> ?</span>

4 0
3 years ago
Solve for x. 8.2x−6.2−7.2x=14 Enter your answer, as a decimal, in the box. x =
slavikrds [6]

Answer is: Solve for x by simplifying both sides of the equation, then isolating the variable.

x = 20.2

6 0
3 years ago
Other questions:
  • A pizza place sells pizzas for $7 each plus a $4 delivery charge per order. If Pat orders 3 pizzas to be delivered, what will be
    15·2 answers
  • Convert: 6y + y² = x² from rectangular to polar form.
    13·1 answer
  • Does anyone know what the answer to this is ?
    9·1 answer
  • Simplify using a table (6q+7)(2q+3)
    5·2 answers
  • The product of 6 and the sum of 3 times a number n and 5
    8·1 answer
  • There were 10 cupcakes on a plate and 7 kids who are trying to share it. How can they share the cupcakes ?
    11·1 answer
  • Given: AC and BC bisect each other at o<br> Prove: ABCD is a parallelogram
    12·1 answer
  • Use the rectangle to answer the question.
    10·2 answers
  • Juan saved x dollers last month. This month he saved $8 more than 3 times the amount he saved last month. he saved a total of $1
    14·1 answer
  • Find the area of the triangle.<br> Height = 4 ft<br> Base = 12 1/2 ft<br> Area = ? square feet
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!