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
A large research hospital is considering a new computer-based training course for lab safety. The total cost of the hospital's c
Katarina [22]
I need that money to but new nikes
8 0
3 years ago
Read 2 more answers
I need help asap :):):):
Kamila [148]

Answer:

its the second one

Step-by-step explanation:

6 0
3 years ago
Solving Quadratic Equations using the Square Root Property
Afina-wow [57]

Answer:

x = -2   or   x = -5

Step-by-step explanation:

You need to complete the square before you can take the square root of both sides.

x^2 + 7x + 10 = 0

Subtract 10 from both sides.

x^2 + 7x = -10

To complete the square, you need to add the square of half of the x-term coefficient to both sides.

The x-term coefficient is 7. Half of that is 7/2. Square it to get 49/4. Now we add 49/4 to both sides of the equation.

x^2 + 7x + \dfrac{49}{4} = -10 + \dfrac{49}{4}

(x + \dfrac{7}{2})^2 = -\dfrac{40}{4} + \dfrac{49}{4}

(x + \dfrac{7}{2})^2 = \dfrac{9}{4}

Now we use the square root property, if

x^2 = k, then

x = \pm \sqrt{k}

x + \dfrac{7}{2} = \pm \sqrt{\dfrac{9}{4}}

x + \dfrac{7}{2} = \pm \dfrac{3}{2}

x + \dfrac{7}{2} = \dfrac{3}{2}   or   x + \dfrac{7}{2} = -\dfrac{3}{2}

x = -\dfrac{4}{2}   or   x = -\dfrac{10}{2}

x = -2   or   x = -5

5 0
3 years ago
Solve: 36(x + 4)= 36
11Alexandr11 [23.1K]

Answer:

x = -3

Step-by-step explanation:

36(x + 4) = 36

Divide both sides by 36

x + 4 = 1

Subtraact 4 from both sides

x = -3

8 0
2 years ago
Read 2 more answers
Determine if the two figures are congruent and explain your answer using transformations.
IRISSAK [1]

Answer:

Comparing each pair of lines,

AB and EF,

BC and FG,

CD and GH,

DA and HE.

For, AB and EF,

If we take a look at both the lines they are the mirror image of each other, the distance between point A and B is 1 unit upwards, and 2 unit sidewise, similarly between point E and F the distance is 1 unit upwards, and 2 unit sidewise. therefore, the length of both the lines is the same.

Also, we can use the formula, for the distance between two points on a coordinate plane,

,

As we can see in the image,

A = (-1, 1),

B = (-3, 2),

C = (-4, 4),

D = (-2, 6),

E = (2, 0),

F = (4, 1),

G = (5, 3),

H = (3, 5),

Solving using the formula,

AB = EF = √5,

BC = FG = √5,

CD = GH = √8,

DA = HE = √26,

Therefore, the length of all the sides of the polygon are the same,

Hence, the two figures are congruent.

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • What number represents the most accurate estimation of 38+23
    12·2 answers
  • Decrease £16870 by 3% Give your answer rounded to 2 DP.
    14·2 answers
  • 3y+2=9x-4 solve for y<br>hurry please
    8·1 answer
  • Write ln (4/9) in terms of ln 2 and ln 3.
    9·1 answer
  • Xminus9yequals<br> 19<br> 8yminus5xequals<br> 16
    10·1 answer
  • What is 6^2/3 in radical form
    8·2 answers
  • What is the length of an arc given that the measure of the central angle is 30 degree and the radius is 7 cm?
    9·1 answer
  • Can someone please help me ASAP ​
    13·2 answers
  • You have a jar of 20 jellybeans with 4 red beans, and you take out 1 red jellybean. Now, after taking out this bean, what is the
    8·2 answers
  • 6n +5&lt;7n + 10
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!