Let the eccentricity of the hyperbola `x^(2)/a^(2) - y^(2)/b^(2) = 1` be reciprocal to that of the ellipse `x^(2) + 4y^(2) = 4`. If the hyperbola passes through a focus of the ellipse, then

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be the reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be the reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be the reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be the reciprocal to that of the ellipse x^(2)+4y^(2)=4 . If the hyperbola passes through a focus of the ellipse, then the equation of the hyperbola, is

The eccentricity of the hyperbola x^2-y^2=4 is

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be reciprocal to that of the ellipse x^(2)+9y^(2)=9 , then the ratio a^(2):b^(2) equals

Let the eccentricity of the hyperbola (x ^(2))/(a ^(2))- (y ^(2))/(b ^(2)) =1 be reciprocal to that of the ellipse x ^(2) + 9y ^(2) =9, then the ratio a ^(2) : b ^(2) equals

Let the eccentricity of the hyperbola (x ^(2))/(a ^(2))- (y ^(3))/(b ^(2)) =1 be reciprocal to that of the ellipse x ^(2) + 9y ^(2) =9, then the ratio a ^(2) : b ^(2) equals

Let e_(1) be the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 and e_(2) be the eccentricity of the ellipse x^(2)/a^2+(y^(2))/(b^(2))=1,a>b ,which passes through the foci of the hyperbola.If e_(1)e_(2)=1 ,then the length of the chord of the ellipse parallel to the "x" -axis and passing through (0,2) is :

If the eccentricity of the hyperbola x^(2) - y^(2) sec^(2)theta = 4 is sqrt3 time the eccentricity of the ellipse x^(2)sec^(2)theta+y^(2) = 16 , then the volue of theta equal