x2/a2+y2/b2=1 has gradient y' given by:
2x/a2+2yy'/b2=0, yy'/b2=-x/a2, y'=-(b/a)2(x/y).
The gradient at (x0,y0) is -(b/a)2(x0/y0). This is m for the tangent line y=mx+c.
The equation of the tangent line is:
y-y0=-(b/a)2(x0/y0)(x-x0), y=y0-(b/a)2(x0/y0)(x-x0), which can be written in various forms. For example:
a2y0=a2y02-b2x0(x-x0)=a2y02+b2x02-b2x0x.
Not sure what you mean by radius m (m is normally the slope or gradient of a line--perhaps "radius"="gradient").