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Prove that the circle x^(2)+y^(2)+2x+2y+...

Prove that the circle `x^(2)+y^(2)+2x+2y+1=0` and circle `x^(2)+y^(2)-4x-6y-3=0` touch each other.

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To prove that the circles given by the equations \(x^2 + y^2 + 2x + 2y + 1 = 0\) and \(x^2 + y^2 - 4x - 6y - 3 = 0\) touch each other, we will follow these steps: ### Step 1: Rewrite the equations of the circles The general form of a circle is given by: \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] We will identify the values of \(g\), \(f\), and \(c\) for both circles. ...
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