Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.
Answers
Answer:
Step-by-step explanation:
Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2
The distance between the focust and the directrix is the value of 2p
Distance beween focus (0,-2) and y=2 is 4
The distance between vertex and focus is p that is 2
Focus is at (0,-2) , so the vertex is at (0,0)
General form of equation is
where (h,k) is the vertex
Vertex is (0,0) and p = 2
The equation becomes
The parabola having like focus (0,p/2) and as directrix y=-p/2 has as equation x²=2py
Here -p/2=2==>p=-4
x²=-8y is the equation.
Related Questions
Factor 3x^2y^2 − 2xy^2 − 8y^2. Show your work.
A container holds 50 electronic components, of which 10 are defective.1. If 6 components are drawn at random from the container, the probability that at least 4 are not defective is ? A) 0.26 B) 0.42 C) 0.75 D) 0.91 E) 1.00 2. If 8 components are drawn at random from the container, the probability that exactly 3 of them are defective is ? A) 0.147 B) 0.203 C) 0.300 D) 0.375 E) 0.750
NEED QUICK 50 POINTS
You can afford a $1400 per month mortgage. You've found a 30 year loan at 7% interest. How big of a loan can you afford?
B. a= 15/2 b= 9/2
C. a= 16/3 b= 15/2
D. a= 9/2 b= 13/2
Answers
THE GREATEST VALUE OF LETTERS
24 = -3 + 3n
b.
11 + 4x = x - 10
c.
-216 = 1 + 7(1 + 8m)
d.
3p - 3(2 - 2p) = 34 + 4p
You must show all of your work to receive credit.
I will give you 27 points if you solve this by showing your work plz
Answers
Answer:
A) n=9
B)X=-7
C)m=-4
D)P=8
Step-by-step explanation:
A)24=-3+3n
move variable to the lefthand side &change its sign
-3n+24=-3
move the constant to the righthand side &change its sign
-3n=-3-24
calculate the difference
-3n=-27
devide both sides by-3
Solution:
n=9
B)11+4x=x-10
11+4x-x=-10
move variable to the lefthand side &change its sign
4x-x=-10-11
move constant to the righthand &change its sign
4x-x=-10-11
collect like terms
3x=-21
devide both sides of the equation by 3
solution :
x=-7
C)-216=1+7(1+8m)
multiply the parentheses by 7
-216=1+7+56m
add the numbers
-216=8m+56m
move variable to the lefthand side &change its sign
-56m-216=8
move constant to the righthand side &change its sign
-56m=8+216
add the numbers
-56m=224
devide both sides of the equation by -56
solution:
m=-4
D)3p-3(2-2p)=34+4p
multiply the parentheses by -3
3p-6+6p=34+4p
collect like terms
9p-6=34+4p
move the variable to the lefthand side &change its sign
9p-4p-6=34
move the constant to the righthand side &change its sign
9p-4p=34+6
collect like terms &calculate the sum
5p=40
devide both sides by 5
solution:
P=8
HiI hope this helps..
After the square undergoes an isometric transformation, its new vertices are Q'(0,0), U'(4,0), A'(4,-4), and D'(0,-4). Which of the following options best describes the type of transformation that maps QUAD onto Q'U'A'D'?
a. reflection
b. translation
c. rotation
Answers
Answer:
Rotation
Step-by-step explanation:
I did odyssey and got it right.
Answers
Roster form or tabular form:
In this, elements of the set are listed within the pair of brackets { } and are separated by commas.
For example:
(i) Let N denote the set of first five natural numbers.
Therefore, N = {1, 2, 3, 4, 5} → Roster Form
(ii) The set of all vowels of the English alphabet.
Therefore, V = {a, e, i, o, u} → Roster Form
(iii) The set of all odd numbers less than 9.
Therefore, X = {1, 3, 5, 7} → Roster Form
(iv) The set of all natural number which divide 12.
Therefore, Y = {1, 2, 3, 4, 6, 12} → Roster Form
(v) The set of all letters in the word MATHEMATICS.
Therefore, Z = {M, A, T, H, E, I, C, S} → Roster Form
(vi) W is the set of last four months of the year.
Therefore, W = {September, October, November, December} → Roster Form
Note:
The order in which elements are listed is immaterial but elements must not be repeated.
Set builder form:
In this, a rule, or the formula or the statement is written within the pair of brackets so that the set is well defined. In the set builder form, all the elements of the set, must possess a single property to become the member of that set.
In this form of representation of a set, the element of the set is described by using a symbol ‘x’ or any other variable followed by a colon The symbol ‘:‘ or ‘|‘ is used to denote such that and then we write the property possessed by the elements of the set and enclose the whole description in braces. In this, the colon stands for ‘such that’ and braces stand for ‘set of all’.
Answers
more than halfway to plotting 'C' and 'D'.
You just have to remember what 'x-coordinate' and y-coordinate' mean.
Whenever a point is described with 2 numbers, the first number is the 'x'
and the second number is the 'y'. You knew that, and that's how you were
able to put 'A' and 'B' in the right places.
Any point: ( x-coordinate, y-coordinate )
Point 'A': (4, 3) ... x-coordinate is 4, y-coordinate is 3 .
Point 'B': (1, -5)... x-coordinate is 1, y-coordinate is -5 .
Point 'C':
has the same x-coordinate as 'B' ... it's 1 .
has the same y-coordinate as 'A' ... it's 3 .
So point 'C' is (1, 3). You should have no trouble marking it on the graph.
An important tip:
When you plot points, you really ought to label them on the graph.
I see the two dots that you put on the graph, but really, the teacher
doesn't know for sure which one you think is 'A' and which one you
think is 'B'. Later, when you get done plotting 'C' and 'D', you'll have
a real mess on the graph if the points are not labeled.
Answers
Final answer:
To meet the conditions for a hypothesistest assuming independent observations, the sample size should have at least five successes and failures, and the population should be at least 10 or 20 times the size of the sample.
Explanation:
In order to meet the conditions for a hypothesistest that assumes independentobservations in the sample, the sample size should be such that each sample has at least five successes and five failures. Additionally, the population must be at least 10 or 20 times the size of the sample to avoid over-sampling and incorrect results.
Learn more about Sample size for independent observations here:
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