math

posted by .

4. In a backyard, there are two trees located at grid points A(-2,3) and B(4,-6).

a) The family dog is walking through the backyard so that it is at all times twice as far from A as it is from B. Find the equation of the locus of the dog. Draw a graph that shows the two trees, the path of the dog, and the relationship defining the locus. Then write a geometric description of the path of the dog relative to the two trees.

b) The family cat is also walking in the backyard. The line segments between the cat and the two trees are always perpendicular. Find the equation of the locus of the cat. Draw a graph that shows the path of the cat. Then write a geometric description of the path of the cat relative to the two trees.

5. A pebble is thrown into a pond at a point that can be considered the origin, (0,0). Circular ripples move away from the origin such that the radius of the circle increases at a rate of 10cm/s.

a) State the equations of the ripples after 1s, after 3s, and after 10s.

1s= x^2+y^=10^2
3s= x^2+y^=30^2
10s= x^2+y^=100^2

is this correct.

b) Descibe the equation of the circle that contains point (-9,12)?

x^2 + y^2 = r^2
-9^2+12^2=r^2
-81+144=r^2
7.94=r

is this right?

c) How many seconds does the ripple take to reach point (-9,12)?

this one i'm stuck..

could you help me?

  • math -

    4a)
    Let the point P(x,y) be a general point on the locus as described

    the AP = BP
    √[(x+2)^2 + (y-3)^2] = 2√[x-4)^2+(y+6)^2]

    square both sides and expand, looks like a circle equation to me

    for b) translate the given condition into a mathematical equation again using a general point P
    isn't the slope(AP) equal to -slopeBP) ??

    for 5a) you forgot the exponent of 2 on the y term, should have been y^2, probably just a typo

    for 5c)
    how long is the radius when you reach (-9,12) ?
    find that length, divide it by 10 cm/s

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    in the backyard there are two trees located at grid points A(-2,3) and B(4,-6) a) The family dog is walking through the backyard so that it is at all times twice as far from A as it is from B. Find the equation of the locus of the …
  2. math

    Marks dog buried 1/2 of his bones in Josh's backyard. He buried 1/3 of his bones in kaylees backyard. he still had 4 bones left to bury. How many bones did Marks dog have in all.
  3. math

    marks dog buried 1/2 of his bones in Jeans backyard. He buried 1/3 of his bones in Mitchell backyard. He still had 4 bones left to bury. how many bones did Marks dog have in all.
  4. Algebra

    I am having a hard time with this problem 3. You are going to plant trees in your hilly backyard. Tree A is located at coordinates (1,2) and Tree B is located at (3,12). What is the slope of the hill between the two trees?
  5. algebra

    3. You are going to plant trees in your hilly backyard. Tree A is located at coordinates (1,4) and Tree B is located at (5,12). What is the slope of the hill between the two trees?
  6. Math

    The Wilson family is putting in a game court in their backyard. The backyard measures 80 feet by 40 feet. The game court will cover 1/5 of the backyard. What is the area of the court?
  7. English

    1. There are five pictures on the pages. Look at the picture on the left page in the middle.....Let's go clockwise. What are they doing?
  8. Math

    A family put a swimming pool in their backyard the rectangular backyard measures 20 by 12. The area of the pool is 1/6 the size of the area of the backyard. what is the area of the pool?
  9. Math

    The Walters' backyard pool is rectangular in shape and is similar to the rectangle formed by their fenced backyard. The pool measures 10 ft long and 8 ft wide. If the length of the backyard is 35 ft long, what is the width of the backyard?
  10. Math

    The Walters' backyard pool is rectangular in shape and is similar to the rectangle formed by their fenced backyard. The pool measures 10 ft long and 8 ft wide. If the length of the backyard is 35 ft long, what is the width of the backyard?

More Similar Questions