Tangent to a point on a circle.

[metachief]

Can anyone explain how to get a tangent line to a circle at a given point on the circle. I tried using the difference quotient, but a calculus example would be better. As well I would like to know how to find the normal to the tangent. Any help or links would be greatly appreciated.

[SJ]

hm, i would use implicit differentiation to find the dy/dx, the slope of the line. from there it's just solving a linear equation. the normal to the tangent is a line with slope -1/m that also passes through the point of tangency: again, solving a linear equation.

[A.J]

You don't need calculus at all for this.

Let's call the center of the circle C and the point on the circle P. Let 'm' be the slope of the line going through C and P. Then, all you have to do is find the equation of a line going through P with slope -1/m (since it is perpendicular to the line CP, the slope is a negative reciprocal of 'm'). No calculus required at all. That's just like trying to kill a fly with a sledgehammer (i.e. overkill)

EDIT : Now that I read SJ's post, it is the same thing. Sorry for the repeat.

[metachief]

Well, the reason for why I mentioned calculus is because I will have to use it to figure out the incident angle between the tangent and the vector at which an aboject will be moving at. I understood how to do it with the dot Product, now all that is left is to find the normal to the point of tangency and send the object at a vector that is the normal of the tangent + the incident angle....

p.s Sometimes flies need be taken care of with sledge hammers to make sure the fly is dead 100%