Equation of circle!!!?

Question

Please help me this exercise!!!!! It is very difficult to me.
Question
Town B is located 36 miles east and 15 miles north of town A.A local telephone company wants to position a relay tower so that the distance from tower to town B is twice the distance from the tower to town A
(A) Show that the tower must be lie on a circle, find the center and radius of this circle.
(B) If the company decides to position the tower on this circle at a point directly east of town A, how far from town A shoul they place the tower?

Answer 1

Town B is 39 miles from Town A:

Use the Pythagorean Theorem: a^2+c^2=c^2
36^2+5^2=c^2
1521=c^2
c=39

So the Tower must be 78 miles from Town B

(B) Town A should be 67.5499815 miles from the tower

78^2=39^2+X^2 ;
where X is equal to the distance of town A to the tower
6084=1521+X^2
X^2= 4563
X=67.5499815

(A)Should Town A&B be lying on the circle the tower is lying on?
If so: then you could make the tower as your center and the radius any distance greater than or equal to the distance from Town B and the Tower

thats all i could say for now hehehe

hope its ok

Answer 2

|z|=2|z+36+15i|

x+yi = 2(x+yi+36+15i)
x+yi = 2(x+36) + 2i(y+15) /(x+yi)
1 = 2(x+36)/(x+yi) +2i(y+15)/(x+yi)

Errr, I don't know anymore. It's been too long. But you have to get a circle equation from that.

No, no. maybe it is the other way around.

x+yi = 2(x+36) + 2i(y+15) / [2(x+36) + 2i(y+15)]
and then you'd get... Ah well, it's your problem.
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Oh, SURE. Use pythagoras then, see if I care. *sniff* If you want to use the proper way the circle equation lookes something like (x-a)²/c² + (y-b)²/d² = 1
c=d because it is a circle ("c" is the radius of the circle) not an ellipse, and and b are x and y coordinates.

Answer 3

I really don't know this but the area of a sphere is the circumfrence but I don't know how to calculate that or this.