Fool's problems of the day,
Today's problems are based on standard analytic geometry,
\((1)\) Find the center of the conic section \(13x^2-18xy+37y^2+2x+14y-2=0 \)
[ Solved by @Mani_Jha and @.Sam. ]
\((2)\) Prove that if the circles \(x^2+y^2+2g_1x+2f_1y+c_1 =0 \) and \(x^2+y^2+2g_2x+2f_2y+c_2 =0 \) are orthogonal then \( 2(g_1g_2 +f_1f_2) = c_1+c_2 \)
[Solved by @Ishaan94]

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@Mani_Jha: Right, do you know why this works? ;)

Atcually, no :\.

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