Finding tangent equation of circle x2 + Y2 + 2x-2y-3 = 0 passing through point (1,2)

Finding tangent equation of circle x2 + Y2 + 2x-2y-3 = 0 passing through point (1,2)

(x+1)²+(y-1)²=5;
The center of the circle is (- 1,1) radius = √ 5;
Tangent slope = - 1 ÷ (2-1) ÷ (1 + 1) = - 2;
-2=(y-2)/(x-1);
-2x+2=y-2;
The tangent is 2x + y-4 = 0;
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