$C$ is the centre of the circle with centre $(0, 1)$ and radius unity. $P$ is the parabola $y = ax^2$. The set of values of $a$ for which they meet at a point other than the origin is

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

If the normal to the rectangular hyperbola $xy = c^2$ at the point $t$ meets the curve again at $t_1$,then $t^3 t_1$ has the value equal to

An ellipse and a hyperbola have the same centre at the origin,the same foci,and the minor axis of the one is the same as the conjugate axis of the other. If $e_1$ and $e_2$ are their eccentricities respectively,then $e_1^{-2} + e_2^{-2}$ equals:

Consider two families of curves $y^2=4ax$ ($a$ is a parameter) and $x^2+\frac{y^2}{2}=c^2$ ($c$ is a parameter). If one curve from each family is chosen, then the angle between those two curves is

The equation of the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is: