$TP$ and $TQ$ are tangents to the parabola $y^2 = 4ax$ at $P$ and $Q$. If the chord $PQ$ passes through the fixed point $(-a, b)$,then the locus of $T$ is:

$AB$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\Delta AOB$ (where $O$ is the origin) is an equilateral triangle. Then the eccentricity $e$ of the hyperbola satisfies:

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

The circle $x^2 + y^2 = 5$ meets the parabola $y^2 = 4x$ at $P$ and $Q$. Then the length $PQ$ is equal to:

If $PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\triangle OPQ$ is an equilateral triangle,where $O$ is the centre of the hyperbola,then the eccentricity $e$ of the hyperbola satisfies: