$A$ parabola passing through the point $(-4, -2)$ has its vertex at the origin and the $y$-axis as its axis. The length of the latus rectum of the parabola is:

Let $A(1, 2)$,$B(4, -4)$,and $C(2, 2\sqrt{2})$ be points on the parabola $y^2 = 4x$. If $\alpha$ and $\beta$ respectively represent the area of $\triangle ABC$ and the area of the triangle formed by the tangents at $A, B, C$ to the parabola,then $\alpha \beta =$

If the focal distance of a point on the parabola $y^2 = x$ is $17/4$,and it lies in the first quadrant,find the equation of the normal at this point.

At which point does the line $x + y = 1$ intersect the parabola $y = x - x^2$?

Suppose $BOAC$ is a rectangle in the $XY$-plane where $O$ is the origin and $A, B$ lie on the parabola $y=x^2$. Then,$C$ must lie on the curve

What is the angle between the tangents drawn from $(1, 4)$ to the parabola $y^2 = 4x$?