Does 2x2 + 2y2 + 3y +10 = 0 represent the equation of a circle? Justify.

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Please find below the solution to the asked query:

General equation of a circle is given by, x2+y2+2gx+2fy+g2+f2-r2=0where r is the radius , and centre of circle is at -g,-fx2+y2+2gx+2fy+c=0c=g2+f2-r2and hence r=g2+f2-cGiven equation, we have2x2+2y2+3y+10=0converting to general form,x2+y2+3y2+5=0comparing with the general equation we have2fy=3y2 or f=342gx=0 or g=0now c=5hence r=g2+f2-c=342-5 = 916-5 which is negative Hence this equation does not represent equation of  a circle

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