"In a private project of mine, I have come across a challenging problem.(adsbygoogle = window.adsbygoogle || []).push({});

I have 3 points: A, B and C.

A is the motionless point of origin and C is the orbital point of destination. B is the linear transmission between the two; it must intersect with the changing position of C after leaving A, accounting for it's continued movement. The issue is, I'm not sure how to calculate whether or not B will meet C given certain values

The equation attached to C should be familiar to most of you; it is the equation of a circle. (Cx-h)^{2}+(Cy-k)^{2}= r^{2}

At the core of my problem is that C is a point moving along this circle at a set rate (call the rate 't')

B, however, is the problem point; B also moves, however it moves from A's a/b to C at a set rate ('s').

This gives us two extra variables:

t = the rate of motion of C's orbit

s = the rate of transmission of B

There are some additional considerations to keep in mind. The line of transmission B moves on (B*) cannot be curved; it must remain linear. I need to figure out how to calculate the equation of this line from A to C given 's'.

So far I have attempted treating the equation of a circle as one point in an equation for a line, however this gives me a range of lines, and from this point I don't know where to go.

y= (xk+√(r^{2}-(Cx-h)^{2})-b)/(h+√(r^{2}-(Cy-k)^{2})-a)+b-(ka+√(r^{2}a^{2}-x^{2}a^{2}+2a^{2}xh-h^{2})-ab)/(h+√(r^{2}-(y-k)^{2})-a)

But this would just give me the range of values given I know the current point of C. does anyone know how I can factor in the travel of C and the movement of B?

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# Help finding the equation of a line to a moving point

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