SOLUTION: Show that the equation {{{(x^2)/(5-C) + (y^2)/(9-C) = 1}}} represents an ellipse if C is any constant less than 5. a hyperbola if C is any constant bewteen 5 and 9. no real locu

Question 473988: Show that the equation represents
an ellipse if C is any constant less than 5.
a hyperbola if C is any constant bewteen 5 and 9.
no real locus if C is greater than 9
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
All you need to know are the general forms of an ellipse and hyperbola. If C > 5, both denominators will be positive; if 5 < C < 9, the 5-C denominator will be negative and 9-C will be positive, and if C > 9, both terms on the LHS will be negative (or zero) and their sum cannot be 1.
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