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

What are the coordinates of the endpoints of the latus rectum of the parabola $(y - 1)^2 = 4(x + 1)$?

If the chord joining the points $(at_1^2, 2at_1)$ and $(at_2^2, 2at_2)$ of the parabola $y^2 = 4ax$ passes through the focus of the parabola,then

From the point $(-1, 2)$, tangents are drawn to the parabola $y^2 = 4x$. The area of the triangle formed by the chord of contact and the tangents is: (in $\sqrt{2}$)

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

The length of the normal chord to the parabola $y^2 = 4x$,which subtends a right angle at the vertex,is