The points $A(1, 2)$,$B(2, 4)$,and $C(4, 8)$ form a/an

If the system of equations $2x + 3y = -1$,$3x + y = 2$,and $\lambda x + 2y = \mu$ is consistent,then:

The equation of the straight line passing through the point of intersection of the straight lines $3x - y + 2 = 0$ and $5x - 2y + 7 = 0$ and having an infinite slope is:

If the lines $ax + by + c = 0$,$bx + cy + a = 0$,and $cx + ay + b = 0$ are concurrent,then:

For all values of $a$ and $b$,the line $(a+2b)x + (a-b)y + (a+5b) = 0$ passes through a fixed point. Find that point.

Let $C$ be the centroid of the triangle with vertices $(3, -1), (1, 3),$ and $(2, 4).$ Let $P$ be the point of intersection of the lines $x + 3y - 1 = 0$ and $3x - y + 1 = 0.$ Then the line passing through the points $C$ and $P$ also passes through the point