The centre of the ellipse $4x^2 + 9y^2 - 16x - 54y + 61 = 0$ is

The equation $\frac{x^{2}}{2-\lambda}-\frac{y^{2}}{\lambda-5}-1=0$ represents an ellipse,if

Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}=1$,where $a > 2$,having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the $y$-axis,be $6 \sqrt{3}$. Then the eccentricity of the ellipse is

The number of values of $c$ such that the straight line $y = 4x + c$ touches the curve $\frac{x^2}{4} + y^2 = 1$ is

$A$ line of fixed length $a + b$, where $a \neq b$, moves such that its ends are always on two fixed perpendicular straight lines. The locus of a point which divides the line into two parts of lengths $a$ and $b$ is

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