from a point P tangents drawn to the circles x^2 + y^2 + x -3=0 ; 3x^2 + 3y^2 -5x +3y=0 :4x^2 +4y^2 +8x +7y +9=0 are of equal length. find the equation of circle through p which touches the line x +y= 5 at point (6,-1)

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Sum of series 2[n/2] ! [n/2]!/ n! [2Co-2C2+3C2....+[-1]^n[n+1]2Cn] where n is an even positive integer. Kindly provide solution of this question and how to generalise this. How do we know that which expansion will give this?

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