The smallest value of $x^2 - 3x + 3$ in the interval $(-3, 3/2)$ is

If the line segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola makes an angle $\theta$ with the positive $X$-axis,then the length of that line segment is

If $x + y = K$ is a normal to the parabola $y^2 = 12x$,then what is the value of $K$?

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 = 4x$,then what is the value of $\frac{1}{m_1} + \frac{1}{m_2}$?

Two perpendicular tangents to the parabola $y^2 = 4ax$ always intersect on the line:

The tangent $PT$ and the normal $PN$ to the parabola $y^2=4ax$ at a point $P$ on it meet its axis at points $T$ and $N$,respectively. The locus of the centroid of the triangle $PTN$ is a parabola whose
$(A)$ vertex is $\left(\frac{2a}{3}, 0\right)$
$(B)$ directrix is $x=0$
$(C)$ latus rectum is $\frac{2a}{3}$
$(D)$ focus is $(a, 0)$