The tangent at the point $(1, 2)$ to the curve $y^2 = 4x$ makes an angle $\theta$ with the positive direction of the $X$-axis. Then $\theta =$ (in $^{\circ}$)

The equation of the tangent to the parabola $y^2=8x$,which is parallel to the line $4x-y+3=0$,is

Tangents drawn from the point $(-8, 0)$ to the parabola $y^2 = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola,then the area of the triangle $PFQ$ (in sq. units) is equal to

The equations of the normals at the ends of the latus rectum of the parabola $y^{2}=4ax$ are given by

The normal at a point on the parabola $y^2=4x$ passes through $(5,0)$. If there are two more normals to this parabola passing through $(5,0)$,then the equation of one of these normals is

Variable chords of the parabola $y^2 = 4ax$ subtend a right angle at the vertex. Then: