A

Suppose a line $p$ passes through the point $A=[2;3]$ and additionally has the property described in the first column of the table. In each row mark the line’s equation. $$\begin{array}{rlrlrl}{p}_1:y& =-3x+9& p_2:y& =x+1& p_3:y& =2x-1\\ p_4:y& =-2x+7& p_5:y& =3& p_6:x& =2\end{array}$$

For each task, select the type of mean you would use to solve it.\[10pt] {\textbf{Note}}: AP -- arithmetic (resp. weighted arithmetic) mean, GP -- geometric (resp. weighted geometric) mean, HP -- harmonic (resp. weighted harmonic) mean.

\kern -2em Let $p$ be a line containing the points $S_4$, $S_1$, $S_3$, $S_2$ in this order, where $|S_4{S}_1|=1\mathrm{cm}$, $|S_1{S}_3|=1.5\mathrm{cm}$, and $|S_3{S}_2|=3.5\mathrm{cm}$. \smallskip Further, let $k_1$, $k_2$, $k_3$, $k_4$, and $k_5$ be circles with the centers $S_1$, $S_2$, $S_3$, $S_4$, and $S_2$ (again) and radii $r_1=3\mathrm{cm}$, $r_2=2\mathrm{cm}$, $r_3=1.5\mathrm{cm}$, $r_4=1.5\mathrm{cm}$, and $r_5=8\mathrm{cm}$ respectively. Determine the relative position of the circles. \kern 6em

In the table, mark a cell, if the two corresponding lines are parallel to each other. $$\begin{array}{rlrlrl}a:& \{\begin{array}{ll}x=3+t\text{, }& \\ y=-3-t;& t\in \mathbb{R}\end{array}& b:& y=3x-2& c:& 4x-2y+5=0\\ d:& y=\frac{2}{3}x-7& e:& 2x+y-6=0& f:& \{\begin{array}{ll}x=3+4t\text{, }& \\ y=\phantom{3}-6t;& t\in \mathbb{R}\end{array}\end{array}$$