If the curves $2x^2 + ky^2 = 30$ and $3y^2 = 28x$ cut each other orthogonally,then $k=$

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

If the tangent to $y^{2}=4ax$ at the point $(at^{2}, 2at)$ where $|t|>1$ is a normal to $x^{2}-y^{2}=a^{2}$ at the point $(a \sec \theta, a \tan \theta)$, then

If the line $y = \sqrt{3}x$ cuts the curve $x^4 + ax^2y + bxy + cx + dy + 6 = 0$ at $A$,$B$,$C$,and $D$,then the value of $OA \cdot OB \cdot OC \cdot OD$ is,(where $O$ is the origin).

The angle between $y^{2}=4x$ and $x^{2}+y^{2}=12$ at a point of their intersection is

The square of the slope of a common tangent drawn to the circle $4x^2 + 4y^2 = 25$ and the ellipse $4x^2 + 9y^2 = 36$ is