If $P(h, k)$ is a point on the parabola $x = 4y^2$ which is nearest to the point $Q(0, 33)$,then the distance of $P$ from the directrix of the parabola $y^2 = 4(x + y)$ is equal to:

The locus of the feet of the perpendiculars drawn from the vertex of the parabola $y^2 = 4ax$ upon all such chords of the parabola which subtend a right angle at the vertex is

If the normal chord drawn at the point $\left(\frac{15}{2}, \frac{15}{\sqrt{2}}\right)$ to the parabola $y^2=15x$ subtends an angle $\theta$ at the vertex of the parabola,then $\sin \frac{\theta}{3}+\cos \frac{2\theta}{3}-\sec \frac{4\theta}{3}=$

If the equation of the parabola,whose vertex is at $(5,4)$ and the directrix is $3x+y-29=0$,is $x^{2}+ay^{2}+bxy+cx+dy+k=0$,then $a+b+c+d+k$ is equal to

The angle of intersection between the curves $y^2 = 4x$ and $x^2 = 32y$ at the point $(16, 8)$ is:

If the tangent to the parabola $4y^2 = x$ makes an angle of $60^{\circ}$ with the $x$-axis,then find its point of contact.