Hyperbola

\(\frac{x^2}{7-\cos ^2 \alpha}-\frac{y^2}{\cos ^2 \alpha}=1\)

\(\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{7-\cos ^2 \alpha}=1\)

\(\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{7+\cos ^2 \alpha}=1\)

\(\frac{x^2}{\cos ^2 \alpha}-\frac{y^2}{5-\cos ^2 \alpha}=1\)