Is x*x + y*y = 0 the equation of the origin (0,0) if x and y =0? If not, why?

I need the reason why my equation cannot be the equation of the origin? Is there any equaion for the origin itself?

Expert Answers

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Assuming that you are, in fact, talking about the equation for a circle, there's another reason why the equation x^2 + y^2 = 0 can't give you the center of the circle at the origin.

If we subtract x^2 from both sides of the equation, we see that y^2 = -(x^2).  But no real number except zero for both x and y will make that equation true.  And those values will give you the origin (0,0) as a solution, but you only have a point--as the earlier answer states, no circle.

What if the values of x and y are not zero?  y^2 still has to have the same value as the opposite of x^2.  We know that squaring a number will never result in a negative number, so the only non-zero values of x and y will be ones in which one of the variables is real and the other is imaginary.  And although we may use our imagination to conjure up a circle, a circle is not composed of imaginary values.

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