Ashwin Muralidharan IIT Madras
Last Activity: 13 Years ago
Hi Amit,
Consider y=mx+c be the line which is a tangent.
For this to be a tangent to any circle,
Make the sub, y=mx+c in the circle equation. You will get a quad in x, which should have only one solution.
And hence the disciminant of that Quad = 0.
So you will get a relation between c and m------ (1)
Also the line should pass through a point (x1,y1). so y1 = mx1+c ---------(2) {Another relation between m and c)
So from 1 and 2, solve for m and c.
Solving between m and c, you should get a quad in m, and hence two values of m, and hence two tangents can be drawn from a point.
And hence you get the equations of the lines.
Hope that helps.
All the best,
Regards,
Ashwin (IIT Madras).