The eccentricity of the ellipse $(x - 3)^2 + (y - 4)^2 = \frac{y^2}{9}$ is

The ellipse having its foci $(0, \pm 1)$ and major axis of length $\sqrt{5}$ is

If the minimum area of the triangle formed by a tangent to the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{4 a^{2}}=1$ and the coordinate axes is $kab$,then $k$ is equal to ..... .

If a number of ellipses are described having the same major axis $2a$ but a variable minor axis,then the tangents at the ends of their latera recta pass through fixed points which are:

For the ellipse given by $\frac{(x-3)^2}{25}+\frac{(y-2)^2}{16}=1$,match the equations of the lines given in List-$I$ with those on the List-$II$.

List-$I$	List-$II$
$(i)$ The equation of the major axis	$(p)$ $3x = 34$
$(ii)$ The equation of a directrix	$(q)$ $y = 2$
$(iii)$ The equation of a latus rectum	$(r)$ $x + y = 9$
	$(s)$ $x = 6$
	$(t)$ $x = 3$
	$(u)$ $3y = 34$

If the tangent at a point on the ellipse $\frac{x^2}{27} + \frac{y^2}{3} = 1$ meets the coordinate axes at $A$ and $B,$ and $O$ is the origin,then the minimum area (in sq. units) of the triangle $OAB$ is