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Find the equations of the tangents to the circle x^{2}+y^{2}-4x-6y-12=0\, and parallel to 4x-3y=1\,.

The given circle is

x^{2}+y^{2}-4x-6y-12=0\, and the line is4x-3y-1=0\,

Any line parallel to the given line is 4x-3y+k=0

Centre of the given circle is (2,3) and radius is {\sqrt  {4+9+12}}=5\,


|{\frac  {4(2)-3(3)+k}{5}}|=5\,

k-1=\pm 25,k=26,-24\,

Hence the required tangent lines are


Main Page:Geometry:Circles