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(i) Show that the equation (x^(2))/(9-c)...

(i) Show that the equation `(x^(2))/(9-c) +(y^(2))/(5-c)=1` represents (a) an ellipse if c is a real constant less than 5 (b) a hyperbola if c is any real constant between 5 and 9.
(ii) Show that each ellipse in (a) and each hyperbola in (b) has foci at the two points `(pm2, 0)` independent of the value of c.

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