If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

The equation of the directrix of the parabola $y^2-x+4y+5=0$ is

If a focal chord of the parabola $y^2 = 4x$ makes an angle $45^{\circ}$ with the positive $X$-axis,then the slopes of the normals drawn at the ends of the focal chord will satisfy the equation:

The equation of the tangent to the parabola $y = x^2 - x$ at the point where $x = 1$ is:

The equation of the latus rectum of the parabola represented by the equation ${y^2} + 2Ax + 2By + C = 0$ is

Find the area of the triangle formed by the tangent and the normal at one end of the latus rectum of the parabola $y^2 = 4ax$ with the axis of the parabola.