A parabola can be drawn given a focus of (4, -8) and a directrix of y=-6
. What can be said about the parabola?
Answers
Answer:
y = 1/4 (x-4)² - 7
Step-by-step explanation:
Point (x , y) on the parabola, focus of (4, -8) and a directrix of y= -6
√(x-4)²+(y- -8)² = √(y- -6)²
(x-4)² + (y+8)² = (y+6)²
(y+8)² - (y+6)² = (x-4)²
(y²+16y+64) - (y²+12y+36) = (x-4)²
y²+16y+64-y²-12y-36 = 4y+28 = (x-4)²
4y = (x-4)² - 28
y = 1/4 (x-4)² - 7
standard formula of parabola: y = a(x-h)² + k (h,k): vertex (4,-7)
The value of equation of parabola is,
⇒ y = 1/4 (x-4)² - 7
What is Parabola?A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line, which is known as the directrix.
Now,
Let a point (x , y) on the parabola, focus of (4, -8) and a directrix of y= -6
Hence, We can formulate;
⇒ √(x-4)²+(y- (-8))² = √(y- (-6))²
⇒ (x-4)² + (y+8)² = (y+6)²
⇒ (y+8)² - (y+6)² = (x-4)²
⇒ (y²+16y+64) - (y²+12y+36) = (x-4)²
⇒ y²+16y+64-y²-12y-36 = 4y+28 = (x-4)²
⇒ 4y = (x-4)² - 28
⇒ y = 1/4 (x-4)² - 7
Thus, The value of equation of parabola is,
⇒ y = 1/4 (x-4)² - 7
Learn more about parabola visit:
https://brainly.com/question/29635857
#SPJ2
Related Questions
I have a 30% off Kohl’s coupon!!! I find a pair of jeans for $29. What would my cost be with the 30% off?
Answers
Answer:
$20.30 plus tax
Step-by-step explanation:
You multiply 28 x .30 and that is your discount.
Answer:
$20.30
Step-by-step explanation:
8rs - 8s= 16p solve for r.
can someone please help/explain?
Answers
Given circle B below, find the value of x.
A 27
B 44
C 71
D 142
Answers
Answer:
B. 44°
Step-by-step explanation:
Central angle = 3x + 10°
Inscribed angle = 2x - 17°
Now
Central angle = 2 * inscribed angle
( Central angle is double of the inscribed angle standing on same arc)
3x + 10° = 2 ( 2x - 17°)
3x + 10° = 4x - 34°
4x - 3x = 34 ° + 10°
x = 44°
Hope it will help :)❤
resuelve la inecuación
(3x<15)
Answers
Answer:
x<5
Step-by-step explanation:
(3x<15)
Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.
x<15/3
Divide 15 by 3 to get 5.
x<5
Explain how to use a number line to find the sum 7 + −2.
Answers
Step-by-step explanation:
start at 7 on the number line. move to the left (because the value is negative) 2 jumps. you will land on 5.
Answer: 5
Step-by-step explanation:
Usually you would just do 7+-2 which is also 7-2 which equals 5 but since it's a number line you do this
You would locate 7 on the number line and do the same for -2
Once done, you would take the distance 2 is from 0 and push 7 there(basically moving it to 5) and that would be how you would use a number line to find the sum of 7 + -2
Now if the 2 was positive, this would be different and you would add the distance making it 9 but since it's negative you push it towards 0 which makes it 5
I hope this helps!
which of the following is equivalent to the expression below when x >0?
Answers
Answer:
C
Step-by-step explanation:
kkgkckyxitxitzoyfoycyoc
There are approximately 3,000 bass in a lake. The population grows at a
rate of 2% per year. What is the average rate of change of the population
of bass from Year 1 to Year 4? Round your answers to the nearest tenth.
Answers
62.4 bass per year from year 5 to year 8, the average rate of change from the population was about 67.6 best per year the change of rate increase was about
It’s not a or c help
Answers
Answer:
D if i'm wrong i'm so sorry
Step-by-step explanation:
Cassandra bought a tablecloth. The area of the tablecloth is 120 ft2. The width of the tablecloth is 10 feet. How long is it?
Answers
the answer is 12 hope this helps!!
Leo is constructing a tangent line from point Q to circle P. What is his next step?
Mark the point of intersection S of the segment created from the arcs and circle R, and construct line RS.
Mark the point of intersection S of circles R and P, and construct line QS.
Construct arcs from point Q that are greater than half the length of segment PQ.
Construct a circle from point P that has a radius of P and the intersection of circles P and R.
Answers
Answer:
hello your question has a missing diagram attached below is the missing diagram
answer :
Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )
Step-by-step explanation:
when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between the given circles and then construct a line through it
Answer:
Mark the point of intersection S of circles R and P, and construct line QS.
Step-by-step explanation:
This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points. If your in FLVS, it would be in lesson 7.04. I also got this right on my test. Good luck!
If the square below is enlarged by a scale factor of 2, what will be the area of the new square? 184 square units 188 square units 192 square units 196 square units
Answers
Answer:
256square units
Step-by-step explanation:
Since we are not given a diagram. Let us assume the side length of the given square is 8 units
If the the square is enlarged by a scale factor of 2, the side length of the new square will be 2 * 8 = 16units
Since area of a square = L²
Hence the area of the new square = 16²
area of the new square = 256 square units
Hence the area of the new square is 256square units
Note that the side length of the original square was assumed. The values can change depending on the side length of the original square before enlargement
❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️❗️Pls hurry I’ll give brailiest ❗️❗️❗️❗️❗️❗️❗️❗️
Answers
Answer: 4 black marbles, 3 blue, 2 green, and one red.
Step-by-step explanation:
can someone help me with this because I am struggling and if you don't mind show me the steps
Answers
Which ordered pair describes the point (2, 5) after a translation of 2 units down and 3
units right?
A (0, 2)
B (5,3)
C (4,2)
D (4,8)
Answers
x = 4 and y = 3.
3x 2 + 5y
A. 27
B. 31
C. 63
D. 159
Answers
Answer:
39
Step-by-step explanation:
I did the math
help me please i love you<33
Answers
Answer:
<B = 95degrees
<D = 137 degrees
Step-by-step explanation:
From the given diagram, the sum of the adjacent sides of the trapezoid is 180degrees. Hence;
<A +<B = 180
85 + <B = 180
<B = 180 - 85
<B = 95degrees
Similarly
<C + <D =180
43 + <D = 180
<D = 180 - 43
<D = 137 degrees
PLEASE PLEASE PLEASEEE HELP I DONT UNDERSTAND
Answers
Answer:
29.5 times pi or 3.14
Step-by-step explanation:
In the equation y = -x + 7 what is the value of m
Answers
y=mx+b
m=-1
I am adding more text to be able to submit this
In the diagram, x is a negative number. and it is closer to zero than y.y is a positive number. which expression must be negative
Answers
Answer:
you already click the answer
Step-by-step explanation:
helpppp me pleaaaaseeeewww
Answers
Answer:
A
Step-by-step explanation:
I believe it is A If I remember correctly
This is my third time asking for helpppppppppp
Answers
Answer:
The new shape will be like the one that i have drawn for you , i think .
Step-by-step explanation:
add two ( to base* from both sides of it * )
delete one ( from hights )
Hope it was useful ;)
6 to the negative 4th power times 6 to the 7th power
Answers
Answer:
216
Step-by-step explanation:
(6 to the -4th) * (6 to the 7th)
Write the standard form of the equation of the circles that passes through (0, 3) with its center at (0,0)
Answers
Answer:
[tex]x^2+y^2=9[/tex]
Step-by-step explanation:
Equation of a circle (when centred at the origin):
[tex]x^2+y^2=r^2[/tex] where r is the radius of the circle
Plug in the point (0,3) to solve for the radius squared
[tex]0^2+3^2=r^2\\9=r^2[/tex]
Plug r² back into the original equation
[tex]x^2+y^2=9[/tex]
I hope this helps!
anyone know the answer?
Answers
Stella wants to buy a $177,000 house, and she is comparing a 7/1 ARM with an interest
rate of 8 75%, amortized over 30 years, with a 7/23 balloon mortgage that has an
interest rate of 8.25%
24. What would Stella's monthly payment be for the 7/1 ARM?
Answers
Answer: Are there any answer choices? If there are I could probably help you, thanks <3
Step-by-step explanation:
Please help fast how to find missing numbers
Answers
Answer:
Step-by-step explanation:
A shirt originally cost $41.10, but it is on sale for $36.99. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent. A. 10% B. 90% C. 11% D. 8%
Answers
Answer:
10%
Step-by-step explanation:
The first step is to calculate the decrease
Original price= $41.10
New price= $36.99
= 41.10-36.99
= 4.11
4.11/41.10 × 100
= 0.1×100
= 10%
Hence the percentage decrease is 10%
The circle graph shows carla's spending. If she spent a total of $320, how much was spent on food?
Answers
Answer:
17, add up all the percentages, then subtract 100 by whatever u got, 100-83= 17
Chloe has enough sand to fill a sandbox with an extra area of 36 square units she wants the outer edge of the sandbox to use as little as Material possible
Answers
Answer:
[tex]Length = Width = 6\ units[/tex]
Step-by-step explanation:
Given
[tex]Area=36[/tex]
Required
The least possible material
Sandboxes usually, are rectangles or squares.
Using the above assumption, the area is calculated as:
[tex]Area= Length * Width[/tex]
[tex]Area= L* W[/tex]
[tex]L * W = 36[/tex]
Make L the subject
[tex]L = \frac{36}{W}[/tex]
The material of the outer edge is calculated by the perimeter.
[tex]Perimeter = 2 * (L +W)[/tex]
[tex]P = 2 * (L + W)[/tex]
Substitute [tex]L = \frac{36}{W}[/tex]
[tex]P = 2 * (\frac{36}{W} + W)[/tex]
Open bracket
[tex]P = \frac{72}{W} + 2W[/tex]
[tex]P = 72W^{-1} +2W[/tex]
To get the minimum material needed, we differentiate P
[tex]P' = -72W^{-2} + 2[/tex]
Set: [tex]P' = 0[/tex]
[tex]-72W^{-2} + 2 = 0[/tex]
Collect like terms
[tex]72W^{-2} = 2[/tex]
Divide both sides by 72
[tex]W^{-2} = \frac{2}{72}[/tex]
[tex]W^{-2} = \frac{1}{36}[/tex]
Rewrite as:
[tex]\frac{1}{W^2} = \frac{1}{36}[/tex]
Take positive square roots of both sides
[tex]\frac{1}{W} = \frac{1}{6}[/tex]
Cross multiply
[tex]W = 6[/tex]
Recall that: [tex]L = \frac{36}{W}[/tex]
So, we have:
[tex]L =\frac{36}{6}[/tex]
[tex]L = 6[/tex]
Hence, the dimension with the littlest material as possible is:
[tex]Length = Width = 6\ units[/tex]
Gilbert purchased a car for 34000. The car depreciates at a rate of 14% per year. The exponential function that represents this situation is y = 34000(0.86)^x.
What is the change factor for this function?
Answers
Answer:
.86
Step-by-step explanation:
Exponential function formula
[tex]y = a ( 1 + or - r ) ^t[/tex]
where a = initial value
r = rate of change
and t = number of years
given the equation y = 34000(0.86)^x.
r = .86
Hence the change factor is .86