The vertex of the parabola $3x - 2y^2 - 4y + 7 = 0$ is

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

If the angle between the tangents drawn to the parabola $y^2 = 4x$ from a point on the line $4x - y = 0$ is $\frac{\pi}{3}$,then the sum of the abscissae of all such points is

The tangent to the parabola $y^2 = 4ax$ at the point $(a, 2a)$ makes an angle with the $x$-axis equal to

From an external point $P(h, k)$,a pair of tangent lines are drawn to the parabola $y^2 = 4x$. If $\theta_1$ and $\theta_2$ are the inclinations of these tangents with the $x$-axis such that $\theta_1 + \theta_2 = \frac{\pi}{4}$,then the locus of $P$ is:

The equation of the given curve is $x^2-4x+4y-8=0$. Match the following:

List-$I$	List-$II$
$(A)$ Focus	$(I)$ $(4,2)$
$(B)$ Vertex	$(II)$ $(3,2)$
$(C)$ One end of the latus rectum	$(III)$ $(2,3)$
$(D)$ Point of intersection of the axis and directrix	$(IV)$ $(2,4)$
	$(V)$ $(2,2)$

The correct matching is: