The ellipse `E_1:(x^2)/9+(y^2)/4=1` is inscribed in a rectangle `R` whose sides are parallel to the coordinate axes. Another ellipse `E_2` passing through the point (0, 4) circumscribes the rectangle `Rdot` The eccentricity of the ellipse `E_2` is `(sqrt(2))/2` (b) `(sqrt(3))/2` (c) `1/2` (d) `3/4`

The ellipse E_(1):(x^(2))/(9)+(y^(2))/(4)=1 is inscribed in a rectangle R whose sides are parallel to the coordinates axes. Another ellipse E_(2) passing through the point (0, 4) circumscribes the rectangle R. The length (in units) of the major axis of ellipse E_(2) is

If the ellipse x^2/a^(2)+y^2/b^(2)=1 is inscribed in a rectangle whose length to breadth ratio is 2 :1 then the area of the rectangle is

If F_1 (-3, 4) and F_2 (2, 5) are the foci of an ellipse passing through the origin, then the eccentricity of the ellipse is

An ellipse has foci (4, 2), (2, 2) and it passes through the point P (2, 4). The eccentricity of the ellipse is

The eccentricity of the ellipse, which passes through the points (2, −2) and (−3,1) is :

The ellipse E:(x^(2))/(25)+(y^(2))/(16)=1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. A hyperbola (with same centre and transverse axis same as major axis of ellipse) intersects the ellipse orthogonally and passes through the vertices of the rectangle.Then eccentricity of the hyperbola is

The eccentricity of the ellipse 5x^(2)+9y^(2)=1 is 2/3 b.3/4 c.4/5 d.1/2

Ellipse x^(2) + 4y^(2) = 4 is inscribed in a rectangle aligned with co-ordinate axes . This rectangle itself is inscribed in another ellipse the passes ellipse that through (-4,0) . Then the equation of the ellipse is