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
If this is equal to 8 find x
dolphi86 [110]
I think it is A. not sure though
8 0
3 years ago
Find two numbers that you can multiply to get a product of 0.56. 0.6 0.7 0.8 0.9 6 7 8 9
Marina86 [1]

Answer:

0.7 and 0.8

Step-by-step explanation:

First you have to use your multiplication table, find out how much equals to 0.56 to make it easer just remove the zero and decimal point for example: 0.56 - 56 then divide it using all numbers. i divided it by 0.8 and is there that number yes and then i got 0.7 and that number is there too.

6 0
3 years ago
Find the solutions of the quadratic equation 6X^2- 6x-2=0
Viefleur [7K]
Hopefully this is good

6 0
3 years ago
Jonas weight 63 pounds. jane weight 67 pounds. round each number to the nearest ten.
IrinaVladis [17]

Answer:

Jonas = 60 pounds

Jane = 70 pounds

Remember- 5 or more, raise the score. 4 or less, let it rest.

Jonas is 63 pounds. 3 is less than 4, so rounded to the nearest ten would be 60 pounds.

Meanwhile, Jane is 67 pounds. 7 is more than 5, so we will raise the score.

So, 67 rounded to the nearest ten would be 70.

You have your answers. 60 and 70. Hope this helps!

4 0
3 years ago
Read 2 more answers
Brainliest to correct quick
musickatia [10]

Answer is <

Why? 1/4 is smaller than 1/2

1/4 can be 4 slices while 1/2 can be 2 slices

2 slices > 4 slices

3 0
2 years ago
Read 2 more answers
Other questions:
  • Solve this equation.<br><br> 23x−15x=x−1<br> A. x=11315<br> B. x=178<br> C. x=1715<br> D. x=78
    7·1 answer
  • A gardener is planting two types of trees:
    11·1 answer
  • Aunt carols peanut brittle recipe calls for 1/3 pound of peanut per batch.If she makes 8 batches how many pounds of peanuts will
    15·2 answers
  • Find the range of the function for the given domain f(x)=4x+8;{-2,-1,0,1,2}
    9·1 answer
  • Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both j
    15·1 answer
  • Need help on this<br><br> Please help
    11·1 answer
  • Find the measure of
    10·1 answer
  • An automobile trip started at 8:35 A.M. and was completed at 2:15 P.M. on the same day. How long did the trip take?
    15·2 answers
  • Solve the simultaneous equations 2x + y = 5 and 2y = x – 10.
    10·2 answers
  • 1/3 x + 4 = x − 2 solve for x
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!