The locus of a point which moves such that the sum of its distances from two fixed points is a constant,is

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 outer ellipse is:

The locus of the mid-points of the chords of an ellipse $x^{2}+4y^{2}=4$ that are drawn from the positive end of the minor axis is

From the point $C(0, \lambda)$,two tangents are drawn to the ellipse $x^2 + 2y^2 = 4$,cutting the major axis at $A$ and $B$. If the area of $\Delta ABC$ is minimum,then the value of $\lambda$ is-

The length of the latus rectum of $16x^2 + 25y^2 = 400$ is

The centre of the ellipse $\frac{(x + y - 2)^2}{9} + \frac{(x - y)^2}{16} = 1$ is