# Coordinates of point on circle certain number of degrees away from other point

I know the center of a circle $(C_x, C_y)$. I know a point on the circle $(X_1, Y_1)$. I want to know the coordinates of a new point on the circle $(X_2,Y_2)$ a certain number degrees $(d)$ away from the original point.

Would this equation be correct?

$$X_2 = C_x + \sqrt{(X_1-C_x)^2+(Y_1-C_y)^2}\cos\left(\arctan\left({y\over x}\right) + d\right)\\[10pt] Y_2 = C_y + \sqrt{(X_1-C_x)^2+(Y_1-C_y)^2}\sin\left(\arctan\left({y\over x}\right) + d\right)$$

So to clarify my question to make sure it is clear, I am starting at a certain point $(X_1,Y_1)$ on a circle (center $C_x,C_y$) and want to travel along the circle a certain number of degrees $(d)$ and come up with the new coordinates at that point $(X_2,Y_2)$

Is the equation I have above correct? And if so, is there a way to make it better/simpler?

• What are $x$ and $y$? What do you do when $x=0$? You can get a much simpler formula by applying a rotation to the initial point.
– amd
Sep 17, 2018 at 23:02
• That is part of my issue. I do not know how to handle that case. How do you apply a rotation to the initial point? That is what I am trying to figure out. Thanks! Sep 18, 2018 at 12:32