The value of $\lambda$ for which the lines $3x + 4y = 5,$ $5x + 4y = 4,$ and $\lambda x + 4y = 6$ meet at a point is

The point of intersection of the lines joining points $\hat{i}+2 \hat{j}, 2 \hat{i}-\hat{j}$ and $-\hat{i}, 2 \hat{i}$ is

If the given lines $y = m_1x + c_1$,$y = m_2x + c_2$,and $y = m_3x + c_3$ are concurrent,then:

If the sum of squares of all real values of $\alpha$,for which the lines $2x - y + 3 = 0$,$6x + 3y + 1 = 0$,and $\alpha x + 2y - 2 = 0$ do not form a triangle is $p$,then the greatest integer less than or equal to $p$ is $.........$

The point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ lies on the line

If the lines $4x + 3y - k = 0$,$2x + y + 3 = 0$,and $3x + 2y + k = 0$ are concurrent,then the perpendicular distance from the point of concurrency of these lines to the line $3x + 4y + 2 = 0$ is