A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.

Answers

Answer 1

Answer:

The equation of the parabola is (x + 4)² = -16(y + 1)

Step-by-step explanation:

The standard form of the equation of the parabola is (x - h)²  = 4p(y - k), where

The vertex of the parabola is (h, k)The focus is (h, k + p)The directrix is at y = k - p  

∵ The focus at (-4, -5)

h = -4

∴ k + p = -5 ⇒ (1)

∵ The directrix at y = 3

∴ k - p = 3 ⇒ (2)

→ Add equations (1) and (2) to find k

∴ 2k = -2

→ Divide both sides by 2 to find k

k = -1

→ Substitute it in equation (1) to find p

∵  -1 + p = -5

→ Add both sides by 1

∴ -1 + 1 + p = -5 + 1

p = -4

→ Substitute the values of h, k, and p in the formula above

∵ (x - -4)² = 4(-4)(y - -1)

∴ (x + 4)² = -16(y + 1)

The equation of the parabola is (x + 4)² = -16(y + 1)


Related Questions

What is the y coordinate of the solution

Answers

Answer:

8

Explanation:

3x-7=x^2-7x+18

X= 5

Y=3(5)-7 aka 15-7

=8

(3x + 6) (5x +4)
I need help I don’t understand

Answers

[tex](3x + 6)(5x + 4) \\ [/tex]

[tex] = 3x(5x + 4) + 6(5x + 4)[/tex]

[tex] = 15 {x}^{2} + 12x + 30x + 24[/tex]

[tex] = 15 {x}^{2} + 42x + 24[/tex]

Find the slope of the line (-4,4) (-3,-2)

Answers

If i help you can you help me

A bag contains exactly three red marbles, five yellow marbles and two blue marbles. If three marbles are drawn from the bag without replacement, what is the probability that all three will be the same color? Express your answer as a common fraction

Answers

Answer:

11/120

Step-by-step explanation:

Red = 3Yellow = 5Blue = 2

Possible options would be red or yellow as only two blue marbles.

Probability of 3 red:

3/10*2/9*1/8 = 1/120

Probability of 3 yellow:

5/10*4/9*3/8 = 1/12

Probability of same three is:

1/120 + 1/12 = 11/120

which of the following is an irrational number?​

Answers

Answer:

B

Step-by-step explanation:

The other choices are terminal numbers which makes them rational numbers but square root of 19 is an irrational number because square root of 19 is 4.3588989.... This makes it an irrational number since it's just random numbers after the decimal point.

B-because the square root of 19,the numbers after the decimal keep going .

Please Help Me. I am so mad at this freaking problem

Answers

G and d is the answer
Thanks
God bless you

True or False: The commutative property allows you to change the order of an addition problem and division problem.
<333

Answers

Answer:

True!!

Step-by-step explanation:

The commutative, associative, and distributive properties help you rewrite a complicated algebraic expression into one that is easier to deal with. When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied.

Hope this helps!! Please consider marking brainliest! Have a good one!!

Complete the pattern. 1, 2, 4, 8, 16, __, __, __

Answers

Answer:

1,2,4,8,16,32,64,128

Step-by-step explanation:

You just multiply the number by two to get the next number in the pattern

Image by Scientif3
Name all of the obtuse angles that share a side with ZVON.
A. ZNOS, ZNOP, ZNOQ, VOS, ZV00, ZVOP
B. ZNOS, ZNOT, ZNOV, ZVOR, ZVOU, ZVOP
C. ZNOS, ZNOT, ZNOR, ZVOR, ZVOQ, ZVOP
D. ZNOS, ZNOT, ZNOU, ZVOR, ZVOQ, ZVOP
Please select the best answer from the choices provided

Answers

I think it’s A it looks like it so I think it is

please solve 2x^2 -4x - 48 = 0

Answers

Answer:

-4, 6

Step-by-step explanation:

[tex]2x^2 -4x - 48 = 0 \\ \\ 2( {x}^{2} - 2x - 24) = 0 \\ \\ {x}^{2} - 2x - 24 = 0 \\ \\ {x}^{2} - 6x + 4x - 24 = 0 \\ \\ x(x - 6) + 4(x - 6) = 0 \\ \\ (x - 6)(x + 4) = 0 \\ \\ x - 6 = 0 \: \: or \: x + 4 = 0 \\ \\ x = 6 \: \:o r \: \: x = - 4 \\ \\ x = - 4, \: \: 6[/tex]

Dionna rode her skateboard at a speed of 10 miles per hour. Which statement is correct?
If she covered 2.5 miles, she rode for 0.25 hours.
If she covered 2.5 miles, she rode for 4 hours.
If she covered 4 miles, she rode for 0.25 hours.
If she covered 4 miles, she rode for 4 hours.

Answers

Answer:

She covered 2.5 miles, she rode for 0.25 hours.

Step-by-step explanation:

0.25*10=2.5

Option A. In 0.25 hours, she rode 2.5 miles.

What is the slope of a line represented by 3x-14y=28

Answers

Answer:

3/14

Step-by-step explanation:

3x-14y=28

solve

add -3 both sides

3x−14y+−3x=28+−3x

−14y=−3x+28

divide both sides by -14

y= 3 /14 x−2

y=mx+b

so 3/14 is the slope

WA store manager records the number of people who have been in his store compared to the number of hours the store has been open. He graphs the data on the scatterplot below and sketches a trend line.

Store Customers

A graph has hours open on the x-axis, and total customers on the y-axis. A trend line goes through points (1, 25) and (2, 50).

Based on the data collected, if the store has been open 7 hours, which scenario is most likely to be true?
After 1/2 hour, 1 customer had been in the store.
After 6 hours, 129 customers had been in the store.
After 7 hours, 175 customers had been in the store.
After 8.5 hours, 225 customers had been in the store.

Answers

Answer: After 7 hours, 175 customers had been in the store.

Step-by-step explanation:

Did the quiz, Trust me.

Answer:

ccccccccc!

Step-by-step explanation:

In his bank account, Jean-Paul has a balance of $0.00
His friend Albert has a bank balance of -$11.10
Which friend's bank account has more debt?


Choose 1 answer:

A. Jean-Paul

B. Albert


Which friend's bank balance has a greater absolute value?

Choose 1 answer:

A. Jean-Paul

B. Albert

Answers

Hey Hey

Answer 1: Jean-Paul (A)
Answer 2: Albert (B)

Hope this helps <3

Answer 1 A
Answer 2 B

CAN SOMEONE HELP ME PLS

Answers

Answer : FAE

EXPLANATION: C. FAE
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