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
frez [133]
2 years ago
12

Write the equation of a parabola with focus at (1,-4) and a directrix at X=2

Mathematics
1 answer:
konstantin123 [22]2 years ago
3 0

Answer:

The equation of a parabola is

x =  \frac{1}{4(f - h)} (y - k) ^{2}  + h

Step-by-step explanation:

(h,k) is the vertex and (f,k) is the focus.

Thus, f = 1, k = −4.

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.

Solving the system, we get h = 3/2, k = -4, f = 1.

The standard form is:

x =  -  \frac{y ^{2} }{2}  - 4y -  \frac{13}{2}

The general form is:

2x +  {y}^{2}  + 8y + 13 = 0

The vertex form is:

x =  -  \frac{(y + 4) ^{2} }{2}  +  \frac{3}{2}

The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.

The focal length is the distance between the focus and the vertex: 1/2.

The focal parameter is the distance between the focus and the directrix: 1.

The latus rectum is parallel to the directrix and passes through the focus: x = 1.

The length of the latus rectum is four times the distance between the vertex and the focus: 2.

The eccentricity of a parabola is always 1.

The x-intercepts can be found by setting y = 0 in the equation and solving for x.

x-intercept:

( -  \frac{13}{2}  \: ,0)

The y-intercepts can be found by setting x = 0 in the equation and solving for y.

y-intercepts:

(0, - 4 -  \sqrt{3)}

(0, - 4 +  \sqrt{3)}

You might be interested in
35 + (45+ 25) = (35 +45) +25 which property is this
Dafna1 [17]

Answer:

Associative Property

Step-by-step explanation:

Commutative: 35+(45+25) = (25+45)+35

Associative: 35+(45+25) = (35+45)+25

Distributive: cannot be done

hope this helps!

8 0
3 years ago
Who’s joe ANSWER AND GET 35 points
slamgirl [31]

Answer:

joe mama-

Step-by-step explanation:

8 0
3 years ago
What is the center and radius of -10x = -121 - y2 - x2 -22y
OlgaM077 [116]

We need to find the center and the radius of

-10x\: =\: -121\: -\: y^2\: -\: x^2\: -22y

The general circle equation is the following

(x-h)^2+(y-k)^2=r^2

where

(h,k) is the center and

r is the radius

1. rearrange the equation

(x^2-10x)+(y^2+22y+121)=0

2. Add 25 on both sides

(x^2-10x+25)+(y^2+22y+121)=25

3. Factor

(x-5)^2+(y+11)^2=5^2

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5

8 0
1 year ago
») Noah finds 14 caterpillars and puts them in 2 cages.
Allisa [31]

Answer:

7 Caterpillars

Step-by-step explanation:

14/2

7 0
3 years ago
Every Sunday, Tamika sells pieces of homemade fudge at a local carnival. Each piece of fudge weighs 34 pound. Next Sunday, Tamik
Aloiza [94]

Answer:

hshshshshshshshsiqkZjfdudiodjfhfbbxdudijdd

5 0
3 years ago
Other questions:
  • This is my last question
    10·2 answers
  • Identify the domain of the function shown in the graph.
    8·1 answer
  • Which equation represents the line that passes through points B and C on the graph?
    11·2 answers
  • Here’s what they are asking
    14·1 answer
  • Help please I have a few minsssssss!!
    13·1 answer
  • What is the correct value of b ?
    10·1 answer
  • Quintin set a goal to do 15 push-ups each day. By how much would he exceed his goal if he did 17 push-ups in a day?
    10·1 answer
  • What is 48:12 simplified
    15·1 answer
  • VERY URGENTTTT PLS HELP!!!!!!!!!!!!!!!!!
    10·1 answer
  • How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!