If you have any function or curve, and a point $(x_0|y_0)$, what formula do you use to determine a point with a specific distance D, on that curve.
Let's say, given an ellipse, you need to determine a function $\theta(t)$, for which $y=a \times sin(\theta(t))$ and $x=b \times cos(\theta(t))$ have a distance D to $v=a \times sin(\theta(t+1))$ and $w=b \times cos(\theta(t+1))$ Meaning, that $\sqrt{(y-v)^2+(x-w)^2}=D$
additionally, I would like to ask, if there is a general formula to solve this for any function? (formula/ way/ algorithm)
Let's say our Point, P, has the co-ordinates, ($x_0 , y_0$), and our curve is f(x,y)=0, and we want a Distance D, from the said point.
Lets say a point q, that satisfies this, has co-ordinates ($x_1,y_1$). As you stated, this would satisfy $f(x_1,y_1)=0$.
For functions of the form $y = f(x)$, we can see that $y_1 = f(x_1)$.
Indeed, we would also want $\sqrt{(x_0-x_1)^2+(y_0-y_1)^2} = D$.
As $y_1 = f(x_1)$, we can substitute this into the above equation, and solve for $x_1$, and the using $y_1 = f(x_1)$, we can obtain $y_1$, and the point, q.
For more complex functions, it can still be possible (for example one can do it with all conic sections, by using the same method.
For other complex functions, I am not sure how it can be done analytically. We can of course apply numerical methods, such as Newton Raphson and Staicase and Cobweb plots.
Hope this helps.