Question 473981
If C < 5, then  ==> 5 - C >0, and 9 - C >0, hence the coefficients will be positive, and we get an equation for an ellipse.

If 5 < C < 9, then 0 > 5 - C > -4, while 4 > 9 - C > 0.  This would give a hyperbola with the y-axis as transverse axis, and the x-axis as conjugate axis.

If C > 9, then both 5 - C and 9 - C are negative, and so the left side of the equation is negative while the right side is positive, a contradiction, hence no real locus is formed.