# 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

$2x+y-6=0\,$

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