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Find the value of lambda if the equation...

Find the value of `lambda` if the equation `(x-1)^2+(y-2)^2=lambda(x+y+3)^2` represents a parabola. Also, find its focus, the equation of its directrix, the equation of its axis, the coordinates of its vertex, the equation of its latus rectum, the length of the latus rectum, and the extremities of the latus rectum.

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