Geo4.42

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Find the equation of the tangent at(1,2) to the circle x^{2}+y^{2}+2x-2y-3=0\,.Find also the equation of the tangent parallel to the above tangent.

The equation of the tangent is

x(1)+y(2)+1(x+1)-1(y+2)-3=0\,

2x+y-4=0\,

Equation of the line parallel to the tangent is

2x+y+k=0\,

Centre of the circle is (1,-1) and radius is {\sqrt  {1+1+3}}={\sqrt  {5}}\,

The distance from the centre to the line is radius

hence

|{\frac  {2(1)-1+k}{{\sqrt  {5}}}}|={\sqrt  {5}}\,

k+1=\pm 5\,

k=4,-6\,

Hence the equation parallel to the above tangent is

2x+y-6=0\,

Main Page:Geometry:Circles