If `e_1a n d\ e_2` are respectively the eccentricities of the ellipse `(x^2)/(18)+(y^2)/4=1` and the hyperbola `(x^2)/9-(y^2)/4=1,` then write the value of `2e_1^ 2+e_2^ 2dot`

If e_1a n d\ e_2 are respectively the eccentricities of the ellipse (x^2)/(18)+(y^2)/4=1 and the hyperbola (x^2)/9-(y^2)/4=1, then the relation between e_1a n d\ e_2 is a. 2e_1 ^2+e_2 ^2=3 b. e_1 ^2+2e_2^ 2=3 c. 2e_1^ 2+e_2 ^2=3 d. e_1 ^2+3e_2 ^2=2

If e_(1) and e_(2) are the eccentricities of the ellipse (x^(2))/(18)+(y^(2))/(4)=1 and the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 respectively and (e_(1), e_(2)) is a point on the ellipse 15x^(2)+3y^(2)=k , then the value of k is equal to

If e and e' are the eccentricities of the ellipse 5x^(2) + 9 y^(2) = 45 and the hyperbola 5x^(2) - 4y^(2) = 45 respectively , then ee' is equal to

The eccentricity of ellipse 4(x-2y+1)^2 +9(2x+y+2)^2=180 is

If e' is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) , then

If the eccentricity of the hyperbola conjugate to the hyperbola (x^2)/(4)-(y^2)/(12)=1 is e, then 3e^2 is equal to:

If e is eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 (where,a lt b), then

If e_(1)ande_(2) be the eccentricities of the ellipses (x^(2))/(a^(2))+(y^(2))/(b^(2))=1and(x^(2))/(a^(2))+(4y^(2))/(b^(2))=1 respectively then prove that 3=4e_(2)^(2)-e_(1)^(2) .

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

If radii of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are in the ratio 1:3 and 4e_(1)^(2)-e_(2)^(2)=lambda , where e_1 and e_2 are the eccetricities of ellipse and hyperbola respectively, then the value of lambda is