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
Lynna [10]
3 years ago
6

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.​

Mathematics
1 answer:
koban [17]3 years ago
3 0

Answer:

x^2 + 4x + y^2 +8y  =  0

Step-by-step explanation:

Given

A = (-1,-2)

B = (2,4)

AP:BP = 1 : 2

Required

The locus of P

AP:BP = 1 : 2

Express as fraction

\frac{AP}{BP} = \frac{1}{2}

Cross multiply

2AP = BP

Calculate AP and BP using the following distance formula:

d = \sqrt{(x - x_1)^2 + (y - y_1)^2}

So, we have:

2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

Take square of both sides

4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2

Evaluate all squares

4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16

Collect and evaluate like terms

4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20

Open brackets

4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20

Collect like terms

4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y  + 20 - 20 =  0

3x^2 + 12x + 3y^2 +24y  =  0

Divide through by 3

x^2 + 4x + y^2 +8y  =  0

You might be interested in
Find gf(2) if f(x)=2x+1,g(x)=3x-2
natali 33 [55]

Answer:

13

Step-by-step explanation:

To find g f(2) , evaluate f(2) and substitute the value obtained into g(x)

f(2) = 2(2) + 1 = 4 + 1 = 5 , then

g(5) = 3(5) - 2 = 15 - 2 = 13

5 0
3 years ago
Directions:Use the product rule to simplify the following monomials.
abruzzese [7]

7) Answer = -24x^8y^{11}

\left(8x^4y^2\right)\left(-3x^4y^9\right)

=-8x^4y^2\cdot \:3x^4y^9

=-24x^4y^2x^4y^9

=-24x^8y^2y^9

=-24x^8y^{11}

8) Answer = -30y^6

2y\left(-5\right)y^2\cdot \:3y^3

=-30yy^2y^3

=-30y^{1+2+3}

=-30y^6

9) Answer = -6x^4y^5

\left(-2xy\right)\left(xy\right)\left(3x^2y^3\right)

=-2xyxy\cdot \:3x^2y^3

=-6xyxyx^2y^3

=-6x^4yyy^3

=-6x^4y^5

3 0
2 years ago
Solve using the guess-and-check strategy.
Nadya [2.5K]
The answer is 12. Matthew would be 12 & Elizabeth would be 7. 12+7=19. So C is your answer. 

7 0
3 years ago
Read 2 more answers
Madeline uses 58 beads to make a necklace she plans to sell 36 necklaces at each craft fair she goes to the summer she plans to
g100num [7]
<h3>♫ :::::::::::::::::::::::::::::: // Hello There ! //  :::::::::::::::::::::::::::::: ♫</h3>

➷  Multiply the number of beads per necklace by the number of necklaces:

58 x 36 = 2088

This is the number of beads needed per each craft fair.

Multiply this value by 4 to get the final value:

2088 x 4 = 8352.

She will need 8352 beads.

<h3><u>❄️</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

5 0
2 years ago
Two girls and two boys went to the festival. The total cost of their tickets was $20. Each child paid the same amount for a tick
sattari [20]

Answer: $5

Step-by-step explanation: 4 children divided by 20 equals 5

6 0
2 years ago
Other questions:
  • 3 folders cost $2.91 which equation would help determine the cost of 2 folders
    6·2 answers
  • How can I simplify these?
    14·1 answer
  • Se vendieron para una función en el teatro 255 entradas a $130,antes del comienzo de la función,hubo 5 devoluciones,pero luego s
    12·1 answer
  • Plz help with both questions
    11·1 answer
  • A line passes through(-3,6) and has slope of -5 what is an equation of the line?
    14·1 answer
  • 3x+4(x+3)=7 solve for x
    9·2 answers
  • Who goes to k12 and is 5 grade I need help
    6·2 answers
  • I need help as soon as possible someone please help
    9·2 answers
  • Ariana earns 20% commission as a salesperson. She sold a ceramic vase that cost $78. How much commission did Ariana earn?​
    10·1 answer
  • Solve this <br> |2x-2|+6b
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!