What is the equation of the chord of contact drawn from the point $(2, 4)$ to the parabola $y^2 = 4x$?

Tangents are drawn at points $(x_i, y_i); i = 1, 2, 3$ lying on the parabola $y = x^2$ to enclose a triangle of area $\Delta$. If $x_1, x_2, x_3$ form an increasing arithmetic progression,where $x_1 = -1$ and $y_3 = 9$,then $\Delta$ is ............. $sq. \, units$.

At what points does the line $2x + y - 1 = 0$ intersect the parabola $y^2 = 4x$?

The equation of the tangent at $(-4, -4)$ on the curve $x^2 = -4y$ is

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

Let $PQ$ and $RT$ be two focal chords of the parabola $y^2=16x$. If $P=(4,8)$ and $R=(16,16)$,then the length of $QT$ is: