The line $y=mx+3$ is tangent to the parabola $y^2=4x$,if the value of $m$ is

The equation of a tangent line to the parabola $y^2 = 8x$,which passes through the point $(1, 3)$,is:

Consider the parabola $25[(x-2)^2+(y+5)^2]=(3x+4y-1)^2$. Match the characteristics of this parabola given in List-$I$ with their corresponding items in List-$II$.

List-$I$	List-$II$
$I$. Vertex	$A$. $8$
$II$. Length of latus rectum	$B$. $(\frac{29}{10}, \frac{-38}{10})$
$III$. Directrix	$C$. $3x+4y-1=0$
$IV$. One end of the latus rectum	$D$. $(\frac{-2}{5}, \frac{-16}{5})$
	$E$. $6$

Find the length of the latus rectum of the parabola $y = x \tan \alpha - \frac{g x^2}{2 u^2 \cos^2 \alpha}$.

If a normal chord of the parabola $y^2 = 4ax$ subtends a right angle at the vertex,its slope is-

If the vertices of a triangle are $(am_1^2, 2am_1), (am_2^2, 2am_2),$ and $(am_3^2, 2am_3),$ then the area of the triangle is