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

Given circle is

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

Centre of the circle is (1,2) and radius is {\sqrt  {1+4+4}}=3\,

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

Now as per the definition of the tangent,

|{\frac  {3(1)-4(2)+k}{{\sqrt  {3^{2}+4^{2}}}}}|=3\,

k-1=\pm 15,k=14,-16\,

The required tangents are


Main Page:Geometry:Circles