A tangent of slope 2 of the ellipse `(x^(2))/(a^(2))+(y^(2))/(1)=1` passes through `(-2, 0)`. Then, three times the square of the eccentricity of the ellipse is equal to

If a tangent of slope 2 of the ellipse (x^2)/(a^2) + (y^2)/1 = 1 passes through the point (-2,0) , then the value of a^2 is equal to

If a tangent of slope 2 of the ellipse (x^2)/(a^2) + (y^2)/1 = 1 passes through the point (-2,0) , then the value of a^2 is equal to

A tangent of slope 2 to the ellipse (x^(2))/(36)+(y^(2))/(49)=1 has an intercept on the y-axis of length

Let there are exactly two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose distance from (0, 0) are equal to sqrt((a^(2))/(2)+b^(2)) . Then, the eccentricity of the ellipse is equal to

Let there are exactly two points on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose distance from (0, 0) are equal to sqrt((a^(2))/(2)+b^(2)) . Then, the eccentricity of the ellipse is equal to

Normal at one end of the latus rectum of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 passes through one end of minor axis, then e^(4)+e^(2)= ( where e is the eccentricity of the ellipse)

An ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through the point (-3,1) and its eccentricity is sqrt(2/5) . The equation of the ellipse is