The tangent to x^{2+y}^2=$a^2$ with slope m is y = mx +/- asqrt(1+$m^2$). The point of tangency for y=mx+asqrt(1+$m^2$) is (-am/sqrt(1+$m^2$), a/sqrt(1+$m^2$)). For circle (x-h)^2+(y-k)^2=$r^2$, the tangent with slope m is y-k = m(x-h) +/- r*sqrt(1+$m^2$). This is used when the slope is specified or when a line from an external point must be tangent.