How do you find the equasion of a tangent line if you know the position, radius, & contact point of a circle?

Answer 1

If you have the center of the circle and the contact point, then you can find the equation of the radius line. The line tangent to the circle with be perpednicular to the radius line.

Answer 2

The equation of a circle with radius r and center (h,k) is:

(x - h)² + (y - k)² = r²

Take the derivative to find the slope. Differentiate implicitly.

2(x - h) + 2(y - k)(dy/dx) = 0
(x - h) + (y - k)(dy/dx) = 0

(y - k)(dy/dx) = -x + h
dy/dx = (-x + h)/(y - k)

So the slope of a tangent line thru a given point (x0,y0) on the circle is:

y - y0 = [(-x + h)/(y - k)](x - x0)

Answer 3

The equation of the circle is (x-h)^2 + (y-k)^2 = r^2, where:
(h.k) is the center of the circle and r is its radius.
The slope at any point of the circle is -y/x .