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hi judgers welcome to another segment of wanna leave memorial high school senior high school math tv and for today we will be discussing the different degenerate cases of a conic section so lets start with the first conic section which is the circle so when do we know that an equation will yield a circle okay so that is our topic for today if the given general equation of a circle will give us a graph of a circle so determining when an equation yields a circle let us go back to the general form of the circle which is x squared plus y squared plus d x plus e y plus f is equal to zero remember that the right side is always equal to zero and if there is a constant number here all we have to do is to transfer that to the left side okay and that becomes the value of f d and e are the coefficients of x and y so why is it important why is d and e important in this equation because d and e will define the center of the circle again so if we are given this general form of the circle this equa