Coordinates of a point at a given distance from (x,y) I seem to have forgotten my coordinate geometry and this is absolutely blank.
Say I have $(x_1,y_1)$ and a distance $d$.
Is it possible for me to solve for what the point $(x_2,y_2)$ is?
To explain more:
If I have
$(x_1,y_1) = (1,2)$, and
$(x_2,y_2) = (3,4)$
Using the distance formula, I can calculate the distance to be $d=2\sqrt2$.
But if I have $(x_1,y_1) = (1,2)$ and $d=2\sqrt2$, how do I recover $(x_2,y_2)$ ?
Edit 
Yes, people are absolutely right when they say, multiple solutions are possible. Still, say, I also have an angle $\theta$ that tells me the orientation. Then, is it still not possible?
 A: No you don't have enough information to recover the $(x_2,y_2)$. The reason is that there are many points around $(x_1,y_1)$ which are a distance $d$ apart from it. In fact all points on the circle of radius $d$ centered at $(x_1,y_1)$ satisfy this. (This in fact the definition of a circle if you think about it.)
However, if you know that this point makes an angle $\theta$ from the $x$-axis, say, then yes you can recover $(x_2,y_2)$. The formula is
$$x_2=x_1+d\times\cos\theta,\quad y_2=y_1+d\times\sin\theta,$$
where $d$ is the distance from $(x_1,x_2)$ to $(y_1,y_2)$.
A: If the billiard table is infinitely large and the ball can not reach to wall, then calculated, the coordinates $(X, Y)$ at which the ball stops can be calculated by the following formula. 
$$
X = L * \cos (θ) + x \\
Y = L * \sin (θ) + y 
$$
But if $a$ (horizontal length), $b$ (vertical length), $x$ (coordinate $x$), $y$ (coordinate $y$), $r$ (radius of the sphere), $θ$ (angle), $L$ (distance until the ball stops) are given then what? 
