The line $y = 2t^2$ intersects the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ in real points if

The longest distance of the point $(a, 0)$ from the curve $2x^2+y^2=2x$ is

Let for two distinct values of $p$ the lines $y=x+p$ touch the ellipse $E: \frac{x^2}{16} + \frac{y^2}{9} = 1$ at the points $A$ and $B$. Let the line $y = x$ intersect $E$ at the points $C$ and $D$. Then the area of the quadrilateral $ABCD$ is equal to

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

If $OT$ is the semi-minor axis of an ellipse,$A$ and $B$ are its foci and $\angle ATB$ is a right angle,then the eccentricity of that ellipse is

If $x+2y+k=0, k>0$ is a tangent to the ellipse $2x^2+y^2=2$,then the equation of the normal to the given ellipse at $\left(\frac{1}{\sqrt{2}}, \frac{k}{3}\right)$ is: