Need intersect point for a line coming from center of circle? [closed]

Question

Closed. This question does not meet Stack Overflow guidelines. It is not currently accepting answers.

---

Questions asking for code must demonstrate a minimal understanding of the problem being solved. Include attempted solutions, why they didn't work, and the expected results. See also: Stack Overflow question checklist

Closed 8 years ago.

Improve this question

I have a line with start point as P1(x1, y1) & end Point as P2(x2, y2). This line is from the center of circle. The circle radius is r. Need a simple equation to identify the circle line intersect point?

Answer 1

Assuming P1 is the center of the circle, first get the slope of the line, then follow it from P1 to distance r along that direction.

phi = atan2(y2-y1, x2-x1)
x = x1 + r * cos(phi)
y = y1 + r * sin(phi)

Answer 2

The equation for a circle is (x-h)^2 - (y-k)^2 = r^2, where the center is (h, k) (which will end up being (0, 0) relative to your line)

Given two points, you can find the slope of the line, now you can plug it into the formula y = m*x + b.

You now have a system of two equations, solve for x or y in one equation, then plug that expression into the other equation and you will find the numeric value of the variable you did not solve for. You can then plug that back into the equation for a line and find the second variable.

Here is the general formula: http://mathworld.wolfram.com/Circle-LineIntersection.html

And some other answers: Circle line-segment collision detection algorithm?