If frac{x^2}{k-frac{5}{2}}+frac{y^2}{frac{7}{ | vedclass

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(C) The given equation is $\frac{x^2}{k-\frac{5}{2}} + \frac{y^2}{\frac{7}{3}-k} = 1$. For this to represent a hyperbola,the denominators must have op

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$\left(-\infty, \frac{7}{3}\right) \cup \left(\frac{5}{2}, \infty\right)$

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(C) The given equation is $\frac{x^2}{k-\frac{5}{2}} + \frac{y^2}{\frac{7}{3}-k} = 1$. For this to represent a hyperbola,the denominators must have opposite signs,i.e.,their product must be negative: $(k - \frac{5}{2})(\frac{7}{3} - k) Multiplying by $-1$,we get $(k - \frac{5}{2})(k - \frac{7}{3}) > 0$. Since $\frac{7}{3} \approx 2.33$ and $\frac{5}{2} = 2.5$,we have $\frac{7}{3} The inequality $(k - \frac{7}{3})(k - \frac{5}{2}) > 0$ holds when $k  \frac{5}{2}$. Thus,the set of all values of $k$ is $\left(-\infty, \frac{7}{3}\right) \cup \left(\frac{5}{2}, \infty\right)$.

If $\frac{x^2}{k-\frac{5}{2}}+\frac{y^2}{\frac{7}{3}-k}= 1$ ($k$ is a real number) represents a hyperbola,then the set of all values of $k$ is

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