If `e` and `e_(1)` are the eccentricities of `xy=c^(2),x^(2)-y^(2)=a^(2)` then `e^(4)+e_(1)^(4)=`

If e_(1) and e_(2) are the eccentricites of hyperbola xy=c^(2) and x^(2)-y^(2)=c^(2) , then e_(1)^(2)+e_(2)^(2)=

If e and e_(1) , are the eccentricities of the hyperbolas xy=c^(2) and x^(2)-y^(2)=c^(2) , then e^(2)+e_(1)^(2) is equal to

If e_(1) and e_(2) are the eccentricities of the hyperbolas xy=9 and x^(2)-y^(2)=25 then (e_(1),e_(2)) lie on a circle c_(1) with centre origin then (radius )^(2) of the director circle of c_(1) is

If e_(1)ande_(2) be the eccentricities of the hyperbola xy=c^(2)andx^(2)-y^(2)=c^(2) respectively then :

If e_(1)&e_(2) are the eccentricities of the hyperbola xy=9 and x^(2)-y^(2)=25 , then (e_(1),e_(2)) lie on a circle c_(1) with centre origin then the (radius)^(2) of the director circle of c_(1) is

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1, then the point ((1)/(e),(1)/(e')) lies on the circle (A) x^(2)+y^(2)=1(B)x^(2)+y^(2)=2(C)x^(2)+y^(2)=3(D)x^(2)+y^(2)=4

e_(1),e_(2),e_(3),e_(4) are eccentricities of the conics xy=c^(2),x^(2)-y^(2)=c^(2),(x^(2))/(a^(2))-(y^(2))/(b^(2))=1,(x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 and sqrt((1)/(e_(1)^(2))+(1)/(e_(2)^(2))+(1)/(e_(3)^(2))+(1)/(e_(4)^(2)))=sec theta then 2 theta is

If e_(1) and e_(2) are the eccentricities of two conics with e_(1)^(2) + e_(2)^(2) = 3 , then the conics are

If e and e' are the eccentricities of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1 and its conjugate hyperbola,the value of 1/e^(2)+1/e^prime2 is