If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\theta =4\] is \[\sqrt{3}\] times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\theta +{{y}^{2}}=16.\] then the value of \[\theta \] equals.

If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}

1.	If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\theta =4\] is \[\sqrt{3}\] times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\theta +{{y}^{2}}=16.\] then the value of \[\theta \] equals.
A.	\[\frac{\pi }{6}\]
B.	\[\frac{3\pi }{4}\]
C.	\[\frac{\pi }{3}\]
D.	\[\frac{\pi }{2}\]
Answer» C. \[\frac{\pi }{3}\]

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If the eccentricity of the hyperbola \[{{x}^{2}}-{{y}^{2}}{{\sec }^{2}}\theta =4\] is \[\sqrt{3}\] times the eccentricity of the ellipse \[{{x}^{2}}{{\sec }^{2}}\theta +{{y}^{2}}=16.\] then the value of \[\theta \] equals.

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