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 R. The eccentricity of the ellispe is

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is (1) x^2+""16 y^2=""16 (2) x^2+""12 y^2=""16 (3) 4x^2+""48 y^2=""48 (4) 4x^2+""64 y^2=""48

The equation of the ellipse whose axes are along the coordinate axes, vertices are (0, +- 10) and eccentricity e = 4/5

If the normal to the ellipse 3x^(2)+4y^(2)=12 at a point P on it is parallel to the line , 2x+y=4 and the tangent to the ellipse at P passes through Q (4,4) then Pq is equal to

Find the equation to the ellipse, whose focus is the point (-1,1), whose directrix is the straight line x-y +3=0, and whose eccentricity is 1/2.

Find the center, foci, the length of the axes, and the eccentricity of the ellipse 2x^2+3y^2-4x-12 y+13=0

A square is inscribed in the circle x^2+y^2-2x+4y+3=0 . Its sides are parallel to the coordinate axes. One vertex of the square is (a) (1+sqrt(2),-2) (b) (1-sqrt(2),-2) (c) (1,-2+sqrt(2)) (d) none of these

If the ellipse x^(2)+2y^(2)=4 and the hyperbola S = 0 have same end points of the latus rectum, then the eccentricity of the hyperbola can be