find the vertex, focus and equation of the directrix for the conic given by (x + 1)^2 = -20(y - 3).
sketch a graph of this conic
Answers
Hello,
The conic is a parabola ,
vertex (-1,3)
focus : (-1,-2)
directrix: y=8
equation: y= - 1/20x²-1/10*x+59/20
solution in picture
The vertex is v(-1,3) , focus is f(-1,8) and the equation of directrix is y = -2.
What is a parabola?A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line. The equidistant from a fixed point called the focus (F), and the fixed-line is called the directrix (x + a = 0).
For the given situation,
The standard form of equation of parabola is given by, [tex]y=\frac{1}{4p}(x-h)^{2}+k[/tex]
The vertex is given by [tex]v(h,k)[/tex]
The focus is given by [tex]f(h,k-p)[/tex]
The equation of directrix is given by [tex]y=k+p[/tex]
The given equation is [tex](x+1)^{2} =-20(y-3)[/tex]
On rearranging the given equation in standard form,
⇒ [tex](x+1)^{2} =-20y+60[/tex]
⇒ [tex](x+1)^{2} -60=-20y[/tex]
Divide by 20 on both sides,
⇒ [tex]\frac{(x+1)^{2}}{20} +4 = y[/tex]
⇒ [tex]y=\frac{-1}{(4)(5)} (x+1)^{2} +3[/tex]
On comparing the above equation with the standard form,we get
[tex]p=-5, h=-1, k=3[/tex]
⇒ [tex]k-p=3-(-5)\ =8[/tex]
Hence we can conclude that the vertex is v(-1,3), focus is f(-1,8) and equation of directrix is y=-2.
Learn more about a parabola here
https://brainly.com/question/7492359
#SPJ2
Related Questions
Angles A and B are complementary. The measure of angle A
is yº. What is the measure of angle B?
Answers
Answer:
D, [tex](90-y)[/tex] degrees
Step-by-step explanation:
Complementary angles are angles that add up to 90 degrees. Since angle A and angle B are complementary, they add up to 90. Since the value of angle A is y degrees, we can substitute y into the equation to get
[tex]y+B=90[/tex]
To get the measure of angle B, we must isolate B.
To isolate B, we have to remove every term from its side.
The only term on the side that B is on other than B is y. To remove y from the left side, we must subtract y from both sides. Doing this will result in the equation:
[tex]B=90-y[/tex]
The only answer option that meets this criteria is D.
if you have a cylindrical tank that's 10 feet long and has a radius of 2 feet, what's the maximum possible capacity of the tank in gallons of water if 1 cubic foot of water = 7.48 gallons? Round your answer to two decimal places.
Answers
Answer:
Step-by-step explanation:
Volume = pi * r^2 * h
r = 2 feet
h = 10 feet
Volume = 3.14 * 2^2 * 10
Volume = 125.6 cubic feet
1 cubic foot contains 7.48 gallons
125.6 cubic feet contain 7.48 * 125.6 = 930.488
The tank contains 930.49 gallons.
please, help! i really need it !! like rnnn!
Answers
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answers
Answer:
(-5,2)
Step-by-step explanation:
Answer:
(5 , 2)
Step-by-step explanation:
F(-5 , 2)
After reflection F'(5 , 2)
The rule for reflection over y-axis is
Original point(x , y) : After reflection: (-x,y)
x-coordinate will change its sign and y-coordinate remains same
Find the volume of the prism.
Answers
Answer:
11,968
Step-by-step explanation:
I'm not sure, but I think its 11,968
PLS HELP ASAP
What are the possible rational zeros of f(x) = x4 + 2x3 − 3x2 − 4x − 12?
Answers
HELLLPPP 31 kilograms is the same as how many pounds? Hint: 1 kg = 2.2 lb Round your answer to the nearest tenth.
Answers
Hi! I'm happy to help!
To solve this, we need to turn all the kilograms into pounds. We know that to turn 1 kg into a pound, you multiply the amount of kilograms by 2.2.
Knowing this, we can multiply our 31 kilograms by 2.2.
31×2.2=68.2
This means that 31 kilograms is equal to 68.2 pounds.
I hope this was helpful, keep learning! :D
Please help! What is 9.6=1/2b show work please!
Answers
Answer:
b = 19.2
Step-by-step explanation:
9.6 = ½b
=> 9.6 × (2/1) = b
=> 9.6 × 2 = b
=> 19.2 = b
Evaluate the expression when x=-6.
x^2-9x+4
Answers
Answer:
- 14
Step-by-step explanation:
x = - 6
x^2 - 9x + 4
= ( - 6 )^2 - 9 ( - 6 ) + 4
= 36 + 54 - 4
= 36 - 50
= - 14
Answer:
[tex]94[/tex]
Step-by-step explanation:
[tex]x^2 - 9x + 4[/tex]
[tex](−6 {)}^{2} −9 (−6) + 4[/tex]
[tex]36 − 9 (−6) + 4[/tex]
[tex]36 + 54 + 4[/tex]
[tex]90+4[/tex]
[tex]94[/tex]
Hope it is helpful....Find the length of side x in simplest radical form with a rational denominator.
4.
609
30°
x
C
Answer: <=
Submit Answer
✓
attempt 1 out of
I really need help with this
Answers
Answer:
x=2
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin 30 = x/4
4 sin 30 =x
4 ( 1/2) =x
2 =x
need help with this!!!
Answers
Answer:
It's D I sure about it correspond means identical... The matching number
4
Select the correct answer.
Simplify the expression. What classification describes the resulting polynomial?
(8x2 + 3x) – (12x2 - 1)
OA.
quadratic binomial
OB. quadratic trinomial
O C.
linear monomial
OD.
linear binomial
Reset
Reset
Next
Answers
Answer:
quadratic trinomial
Step-by-step explanation:
(8x^2 + 3x) – (12x^2 - 1)
Distribute the minus sign
8x^2+3x-12x^2+1
Combine like terms
-4x^2+3x+1
This is a quadratic since the highest power of x is 2
This is a trinomial since there are 3 terms
can you help me please.
Answers
hope this helps :)
Answer:
45
Step-by-step explanation:
1st term is 2
2nd term is 3
3rd term is 4
.
.
.
nth term is (n+1)
because common difference is 1, so 1st term = 1 + common difference = 1+1 = 2, for any term, we take n + common difference, so n+1
putting n = 44,
44th term is 44+1 = 45
Answered by GAUTHMATH
The population of Greater Accra increased by 20% and became 900,7000. The original population of the city was:
Answers
Answer:
the original population of the city is 7,505,833
Step-by-step explanation:
Given;
new of the population of the city, Y = 9,007,000
the percentage increase of the city, = 20% = 0.2
Let the original population of the city = X
New population, Y = X + 0.2X
Y = X(1 + 0.2)
Y = X(1.2)
Y = 1.2X
X = Y/1.2
X = (9,007,000) / 1.2
X = 7,505,833
Therefore the original population of the city is 7,505,833
the perimeter The area of squre Plat is 100 m² Find at the plot o a
Answers
Answer:
perimeter=40m
Step-by-step explanation:
PERIMETER=(AREA ROOT)*4
=10*4=40m
Can someone explain this / answer, Its a picture
Answers
Answer:
option c is the correct answer (l=1 cm and w=42cm)
Step-by-step explanation:
length(l) = 1.00cm
width(w)= 42.00 cm
ACCORDING TO FORMULA
Area of rectangle = l×w
=1 cm × 42 cm
= 42cm^2
Simplify to create an equivalent expression.
2(3y + 6) - 3(-4- y)
Choose 1 answer:
gy
5y + 24
9y - 24
9y + 24
Answers
Answer:
9y + 24
Step-by-step explanation:
2(3y + 6) - 3(-4 - y)
= 6y + 12 - 3(-4 - y)
= 6y + 12 + 12 + 3y
= 9y + 12 + 12
= 9y + 24
determine the quadratic equation in standard form of a parabola with a zero at x=5 and vertex ar (-3, 32). start with factored form
a)find the other zero
b) create your factored form equation
c) create your standard form equation
Answers
Answer:
see image...
start with Graphing Form: y = a(x-h)²+ k
knowing that h is the x value (negative of it) of the vertex , and k is the y value of the vertex
Graphing Form Equation: y = a(x+3)²+32
you are also given that when the x value is 5 the y value has to be 0
0 = a(4)^2 + 32
a has to be - 1/2
Step-by-step explanation:
Work out the value of 10^2 - 4^3
Give your answer as a power of 6.
Answers
Answer:
6^2 = 36
Step-by-step explanation:
10^2 = 10 * 10 = 100
4^3 = 4 * 4 * 4 = 64
10^2 - 4^3= 100 - 64 = 36 = 6^2
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]6^2[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\10^2 - 4^3\\---------------\\\rightarrow 10^2 = 100\\\\\rightarrow 4^3 = 64\\\\\rightarrow 100 - 64 = \boxed{36}\\\\\text{Since we know that '36' is a perfect square, we can rewrite our answer as: } \boxed{6^2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
please help me !! :)
Answers
What is the answer for this question
Answers
Answer:
option d. is the correct answer
Which label on the cone below represents the center of the base?
D
B
Ο Α
OB
Answers
Answer:
C
Step-by-step explanation:
The center of the base is the center of the circle
The center of the circle is C
On a coordinate plane, a parabola opens up. Solid circles appear on the parabola at (negative 4, 14), (negative 3, 9.5), (negative 2, 6), (0, 2), (1, 1.5), (2, 2), (4, 6), (5, 9.5), (6, 14).
Which is the rate of change for the interval between 2 and 6 on the x-axis?
Answers
Answer:
Step-by-step explanation:
The rate of change for the interval between x = 2 and x = 6 is simply asking you for the slope of the line that connects these 2 coordinates. If you were in calculus, you could find the instantaneous slope at any point on this parabola, but you're not quite that lucky yet, so we will go about it the only way we can:
by finding the slope. Remember, that slope is the same thing as rate of change.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and filling in:
[tex]m=\frac{14-2}{6-2}=\frac{12}{4}=3[/tex]
A rectangular school yard has a perimeter of 114 meters and an area of 702 square meters. What are the dimensions of the school yard?
Answers
Reason:
2x+2y=114 (perimeter)
XY=702 (area)
X=18
Y=39
One of the lengths of a leg on a right angled triangle is 15 ft the length of the hypotenuse is 17 ft find the length of the other leg
Answers
What is the slope of the line shown below?
10+
5
(9, 1)
o A. -
OB.
OC
10
15
(-3,-7) 5
10
O
D.
WIN
Answers
Answer:
D 2/3
Step-by-step explanation:
Rise over run. The x values is -3 and 9 which is the distance or run between the dots. Find the distance by finding which number is between then so -3+x=9 where x is 12. The y values are -7 and 1. Find y where -7+y=1 where y is 8. That is the rise. So the rise is 8 and that is over the run, 12, gives you 8/12 which can be simplified to 2/3.
I need help ASAP!! Please explain how to solve the problem
Answers
Answer:
Step-by-step explanation:
Surface Area of Cylinder = 2πrh+2πr^2
2π(3)(12) + 2π(3)^2
= 282.7 yd^3
answered by g a u t h m a t h
Rotate the vector 3,-2 90 degrees clockwise about the origin.
Answers
Answer:
-2,-3
Step-by-step explanation:
Answer:
-2 -3
It worked for me on acellus
Step-by-step explanation:
If the point (b,15) lies on the straight line with equation Y=5x fonde the value of b ?
Answers
Answer:
b = 3
Step-by-step explanation:
Substitute the y- coordinate 15 into the equation , that is
15 = 5x ( divide both sides by 5 )
3 = x
This is the x- coordinate of the point , so b = 3
Put the following equation below in function notation and evaluate, using x as the independent
variable.
3x + 5y = 15; x=2
Answers
Answer:
1st option
Step-by-step explanation:
3×2+5y=15
5y=15-6
y=9/5
Answered by GAUTHMATH
Here it is
Hope it helps
