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
Firlakuza [10]
3 years ago
5

Write the equation of a parabola with a vertex at (-5, 2) and a directrix y = -1.

Mathematics
1 answer:
ankoles [38]3 years ago
4 0
The vertex is halfway between focus and directrix, so we know the focus is at (-5,5).
Points on the parabola have the form (x, f(x)). They all have equal distance to the focus and the directrix, so they satisfy the following equation:
f(x) - (-1) = sqrt( ( x - (-5) )^2 + (f(x) - 5)^2)
(Left side is distance to directrix, only depends on the y-coordinate of the point. Right side is the distance between point an focus computed using the pythoagorean theorem.)
Squaring both sides  and collecting the minuses gives
(f(x) +1)^2 = ( x + 5 )^2 + (f(x) - 5)^2
Multiply out the brackets using the binomial theorem:
f(x)^2 + 2*f(x) + 1 = x^2 + 10x + 25  + f(x)^2 - 10f(x) + 25
Simplify by subtracting f(x)^2. Then bring +1 to the right side and -10f(x) to the left side. This gives
12*f(x) = x^2 + 10 x + 49
Divide by 12 and you get the final function:
f(x) = 1/12 *x^2 + 10/12 * x + 49/12


You might be interested in
A bakery sells 3 muffins for every 5 pizza pies.The bakery sold a total of 24 muffins and pizzas pies together.how many of each
Rudiy27

Number of muffins sold=9

and number of pizza pies sold=15

8 0
3 years ago
What is 10+2<br> just trying to give people more points!!
Sergio039 [100]

Answer:

12

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Suppose C and D represent two different school populations where C &gt; D and C and D must be greater than 0
tensa zangetsu [6.8K]

Answer:

Step-by-step explanation:

8 0
3 years ago
Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2
kow [346]
Well knowing that the terminal arm of the standard position angle is in quadrant 2, we can determine the reference angle, in quadrant 2, by simply taking the difference between 180 and whatever the angle is.

So ø reference = 180 - ø in standard position.

Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.

Solve for adjacent side using Pythagoras theorem.

A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.

Then write the cos ratio using the new side.

Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.
3 0
3 years ago
In the right triangle, what is sin (k)
umka2103 [35]

Answer:

Sine is a trigonometric ratio comparing two sides of a right triangle. Sine is usually shortened to sin but is pronounced sine. This function can be used to determine the length of a side of a triangle when given at least one side of the triangle and one of the acute angles

Step-by-step explanation:

hope this helps

7 0
2 years ago
Other questions:
  • Which of these ratios is NOT in simplest form? 4/9 11/13 6/5 14/21
    14·2 answers
  • Find the equation of the line in standard form containing a point P(-3.3) and slope m= -4/3<br><br>​
    11·1 answer
  • What is the answer for this 3/8% as a fraction
    12·2 answers
  • (2a+b)^2 simplest form
    12·1 answer
  • Which list shows the absolute values in order from least to greatest?
    10·2 answers
  • Don't mind the other one i click it was on mistake!
    7·1 answer
  • If = and x &gt; 0 what is the value of x ?
    15·1 answer
  • Please help marking brainliest QUICK
    14·2 answers
  • Which of the following represents "next integer after the integer n"?<br> On<br> On + 1<br> O2n
    12·1 answer
  • What is parallel to 5x+2y=8
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!