The line Ax+By=C (with C nonzero) is tangent to some circle centered at the origin.
What is the radius of that circle in terms of A, B, and C?
What is the point of tangency in terms of A, B, and C?
ax + by = c
slope = -a/b
perpendicular line through origin:
y = bx/a
which intersects original line by solving
ax + (b^2)x/a = c
(a+(b^2)/a)x = c
x = c/(a+(b^2)/a) = ca / (a^2+b^2)
y = bca / (a*(a^2+b^2))
Point of tangency:
(ca / (a^2+b^2), bca / (a*(a^2+b^2))
The radius of the circle can be found from the pythagorean theorem applied to these x and y coordinates.
Edited on January 5, 2017, 12:09 pm
Posted by Charlie
on 2017-01-04 13:38:09