" 3.The director circle of the ellipse "(x^(2))/(a^(2))+(y^(2))/(b^(2))=1" is "

Equation of director circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

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

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

If the area of the auxillary circle of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

If the area of the auxilliary circle of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 (a gt b) is twice the area of the ellipse, then the eccentricity of the ellipse is

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

The locus of the poles of tangents to the director circle of the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 with respect to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 is

The director circle of the ellispe x^(2)/9 + y^(2)/5 = 1