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

Find the axis of the parabola $9y^2 - 16x - 12y - 57 = 0$.

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. If another tangent is drawn to the parabola from a point on this line such that it is perpendicular to the given tangent,find the point.

What is the slope of the tangents drawn from $(3, 8)$ to the parabola $y^2 = -12x$?

Let $A, B$ and $C$ be three points on the parabola $y^2=6x$ and let the line segment $AB$ meet the line $L$ through $C$ parallel to the $x$-axis at the point $D$. Let $M$ and $N$ respectively be the feet of the perpendiculars from $A$ and $B$ on $L$. Then $\left(\frac{AM \cdot BN}{CD}\right)^2$ is equal to...........

The curve described parametrically by $x = t^2 + t + 1$ and $y = t^2 - t + 1$ represents: