For the hyperbola $\frac{x^2}{9} - \frac{y^2}{3} = 1$,the incorrect statement is:

Find the area of the region enclosed by the equation $2|x| + 3|y| = 6$ in square units.

Through the vertex $O$ of the parabola $y^2 = 4ax$,two chords $OP$ and $OQ$ are drawn,and the circles on $OP$ and $OQ$ as diameters intersect in $R$. If $\theta_1, \theta_2$,and $\phi$ are the angles made with the axis by the tangents at $P$ and $Q$ on the parabola and by $OR$ respectively,then the value of $\cot \theta_1 + \cot \theta_2$ is:

If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide,then $b^2$ is equal to

Let $L$ be a tangent line to the parabola $y^{2}=4x-20$ at the point $(6,2)$. If $L$ is also a tangent to the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{b}=1$,then the value of $b$ is equal to ..... .

Match the following parametric forms in List-$I$ with their corresponding conic sections in List-$II$:

List-$I$	List-$II$
$(A)$ $\left[\frac{p}{2}\left(t+\frac{1}{t}\right), \frac{q}{2}\left(t-\frac{1}{t}\right)\right]$	$(I)$ parabola
$(B)$ $(p+q \cos \theta, r+q \sin \theta)$	$(II)$ circle
$(C)$ $(p+\lambda^2, q-\lambda)$	$(III)$ ellipse
	$(IV)$ hyperbola