math
posted by Lucy on .
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?

4a)
Let the point P(x,y) be a general point on the locus as described
the AP = BP
√[(x+2)^2 + (y3)^2] = 2√[x4)^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