The points on the ellipse $$16 x^2+9 y^2=400$$ at which the ordinate decreases at the same rate at which the abscissa increases are

If an ellipse has an equation in the standard form and it passes through the points $$\left(\frac{5}{2}, \frac{\sqrt{6}}{4}\right)$$ and $$\left(-2, \frac{\sqrt{15}}{5}\right)$$ then the length of its latus rectum is

The equation of an ellipse, whose focus is $$(1,0)$$, directrix is $$x=4$$ and whose eccentricity is a root of the quadratic equation $$2 x^2-3 x+1=0$$, is

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is