If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 = 4x$,then what is the value of $\frac{1}{m_1} + \frac{1}{m_2}$?

If the line $lx + my + n = 0$ is a tangent to the parabola $y^2 = 4ax$,then the locus of its point of contact is

If $x-2=t^2$ and $y=2t$ are the parametric equations of the parabola $y^2=a(x-b)$,then the value of $a+b$ equals

Consider the circle $C: x^2+y^2=4$ and the parabola $P: y^2=8x$. If the set of all values of $\alpha$,for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha, 0)$ are bisected by the parabola $P$,is the interval $(p, q)$,then $(2q-p)^2$ is equal to.............

The points of contact $Q$ and $R$ of the tangents drawn from the point $P(2, 3)$ to the parabola $y^2 = 4x$ are

Let $P(\alpha, \beta)$ be a point on the parabola $y^2 = 4x$ which is at minimum distance from the circle $x^2 + y^2 - 4x - 20y + 103 = 0$. Then $\alpha \beta$ is