If a normal drawn to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ meets the parabola again at $(at^2, 2at)$,then the value of $t$ is:

The condition for the line $y=mx+c$ to be a normal to the parabola $y^{2}=4ax$ is

If one end of a focal chord $AB$ of the parabola $y^{2}=8x$ is at $A\left(\frac{1}{2},-2\right)$,then the equation of the tangent to it at $B$ is:

The equation of the chord of contact of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 + x = 0$ is:

The length of the latus-rectum of the parabola whose focus is $\left( \frac{u^2}{2g} \sin 2\alpha, -\frac{u^2}{2g} \cos 2\alpha \right)$ and directrix is $y = \frac{u^2}{2g}$,is

The tangent at the point $(1, 2)$ to the curve $y^2 = 4x$ makes an angle $\theta$ with the positive direction of the $X$-axis. Then $\theta =$ (in $^{\circ}$)