The ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` is such that its has the least area but contains the circel `(x-1)^(2)+y^(2)=1`
The length of latus of ellipse is

The ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is such that it has the least area but contains the circle (x-1)^(2)+y^(2)=1 The eccentricity of the ellipse is

The area of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is

If the length of minor axis of the ellipse (x^(2))/(k^(2)a^(2))+(y^(2))/(b^(2))=1 is equal to the length of transverse axis of hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 ,and the equation of ellipse is confocal with hyperbola then the value k is equal to

If eccentricity of the ellipse (x^(2))/(a^(2)+1)+(y^(2))/(a^(2)+2)=1 is (1)/(sqrt6) , then the ratio of the length of the latus rectum to the length of the major axis is

For the ellipse (x^(2))/(4) + (y^(2))/(3) = 1 , the ends of the two latus rectum are the four points

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(b^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

Area of the ellipse x^2/a^2+y^2/b^2=1 is piab

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which has O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

A O B is the positive quadrant of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 in which O A=a ,O B=b . Then find the area between the arc A B and the chord A B of the ellipse.

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these