If $e$ and $e^{\prime}$ are the eccentricities of the ellipse $5x^2 + 9y^2 = 45$ and the hyperbola $5x^2 - 4y^2 = 45$ respectively,then $ee^{\prime}$ is equal to

If two curves $x^2-4y^2=2$ and $8x^2=40-my^2$ are orthogonal to each other,then $m=$

If $S \equiv \frac{x^2}{k-7}+\frac{y^2}{11-k}-1=0, k \in R-\{7,11\}$,then which one of the following statements is incorrect?

The equation of a common tangent to the parabola $y^2 = 4x$ and the hyperbola $xy = 2$ is

If the curves $y^2=16x$ and $9x^2+\alpha y^2=25$ intersect at right angles,then $\alpha=$

Let the circle $C$ touch the line $x - y + 1 = 0$,have the centre on the positive $x$-axis,and cut off a chord of length $\frac{4}{\sqrt{13}}$ along the line $-3x + 2y = 1$. Let $H$ be the hyperbola $\frac{x^2}{\alpha^2} - \frac{y^2}{\beta^2} = 1$,whose one of the foci is the centre of $C$ and the length of the transverse axis is the diameter of $C$. Then $2\alpha^2 + 3\beta^2$ is equal to . . . . . .