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
SCORPION-xisa [38]
3 years ago
5

The x- and y-coordinates of the focus of a parabola are (1,3) and the directrix is y=-5 . A second parabola is a translation 1 u

nit right and 2 units up of the first parabola. Write an equation of the second parabola.
Mathematics
1 answer:
Marianna [84]3 years ago
7 0

Answer:

The equation of the second parabola is y=\frac{1}{16} \left(x - 2\right)^{2} + 1

Step-by-step explanation:

We know that the focus of the first parabola is (1,3) and the directrix is y = -5. We also know that the second parabola is a translation 1 unit right and 2 units up of the first parabola.

We can use the focus of the first parabola to find the focus of the second parabola (1+1, 3+2) = (2, 5) and the directrix of the second parabola is moved 2 units up. The equation of the directrix of the second parabola is y = -3.

To find the parabola equation we start by assuming a general point on the parabola (x,y).

Next, with the help of the distance formula we find that the distance between (x,y) and the focus.

\sqrt{(x-2)^2+(y-5)^2}

The distance between (x,y) and the directrix y = -3 is \sqrt{(y+3)^2}

On the parabola, these distances are equal:

\sqrt{\left(y+3\right)^2}=\sqrt{\left(x-2\right)^2+\left(y-5\right)^2}\\\left(\sqrt{\left(y+3\right)^2}\right)^2=\left(\sqrt{\left(x-2\right)^2+\left(y-5\right)^2}\right)^2\\\\\left(y+3\right)^2=\left(x-2\right)^2+\left(y-5\right)^2\\\\\left(y+3\right)^2= x^2-4x+4+y^2-10y+25\\\left(y+3\right)^2=x^2-4x+y^2+29-10y\\\\y^2+6y+9=x^2-4x+y^2+29-10y\\16y=x^2-4x+20\\y=\frac{x^2-4x+20}{16}\\\\y=\frac{1}{16} \left(x - 2\right)^{2} + 1

The equation of the second parabola is y=\frac{1}{16} \left(x - 2\right)^{2} + 1

You might be interested in
If f(x) = 2x - 6 and g(x) = 3x + 9, find (f + g)(x)
alex41 [277]

Answer:

5x+3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) \\  =2x - 6 + 3x + 9 \\  = 5x + 3

consider marking as Brainliest if this helped

5 0
3 years ago
Cole has a rectangular garden with an area of 16.02 square meters. What is the width, in meters, of the garden?
exis [7]

Answer:

3.56m

Step-by-step explanation:Parameters given:

Area of the rectangular garden = 16.02m^2

Length of the rectangular garden = 4.5m

The Area of a rectangle can be calculated for using the formula below

Area (square meters) = length (meters) × width (meters)

Therefore, 16.02m^2 = 4.5m × width

Width = 16.02m^2 / 4.5m

Width = 3.56m

Therefore the width in meters of the garden is 3.56m

See the attachment below for an illustrative diagram

A = area

l = length

w = width

8 0
3 years ago
Read 2 more answers
The frequency distribution shows the lengths, in inches, of available baseball bat at a batting cage. what is the mean of the fr
ivanzaharov [21]
The mean of a frequency distribution is given by
<span>
\bar{x}= \frac{\Sigma fx}{\Sigma f} \\  \\  = \frac{(27\times2)+(28\times5)+(31\times3)+(33\times1)+(34\times4)}{2+5+3+1+4} \\  \\  = \frac{54+140+93+33+136}{15} = \frac{456}{15} =30.4</span>
6 0
3 years ago
The value of y varies directly with the value of x. When y = 32.5, x = 5. What is the value of y when x = 10?
Dafna1 [17]
10 is double 5 so,
32.5 multiplied by 2 is: 65
answer: 65
5 0
3 years ago
Read 2 more answers
I need help it's really hard<br>Properties of exponents
Agata [3.3K]

\bf 12^x\times 12^4=12^8\implies \stackrel{\textit{if the base is the same, so are the exponents}}{12^{x+4}=12^8} \\\\\\ x+4=8\implies x=4

3 0
3 years ago
Other questions:
  • The 102nd floor of the sears tower in chicago is the highest occupied floor. it is 1,431 feet above the ground. how many yards a
    10·1 answer
  • Help me please. I am having troubles with my math homework.
    11·1 answer
  • Does (-2)^n/( 3^n+1) converge or diverge?
    7·1 answer
  • How do you write 3,246.78 in expanded form using base 10
    13·1 answer
  • 2. Jon is firing his slingshot towards a tree, when suddenly gravity on the earth disappears.
    7·1 answer
  • The scale of a map is 0.5 inch: 50 miles. on the map, the distance between two cities is 5 inches. what is that actual distance
    8·1 answer
  • Which is closest to the mean number ??
    15·1 answer
  • In the diagram, N, O, and P are congruent. Find x.
    9·1 answer
  • 1. En una biblioteca quieren comprar una computadora que
    9·1 answer
  • Due urgently if not done I’m gonna failllll<br><br> Pre-Algebra<br> Due TODAY
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!