Suppose $$P$$ and $$Q$$ lie on $$3 x+4 y-4=0$$ and $$5 x-y-4=0$$ respectively. If the mid-point of $$P Q$$ is $$(1,5)$$, then the slope of the line passing through $$P$$ and $$Q$$ is

The length of intercept of $$x+1=0$$ between the lines $$3 x+2 y=5$$ and $$3 x+2 y=3$$ is

Suppose the slopes $$m_1$$ and $$m_2$$ of the lines represented by $$a x^2+2 h x y+b y^2=0$$ satisfy $$3\left(m_1-m_2\right)-7=0$$ and $$m_1 m_2-2=0$$. Then, which of the following is true?

Suppose that the sides passing through the vertex $$(\alpha, \beta)$$ of a triangle are bisected at right angles by the lines $$y^2-8 x y-9 x^2=0$$. Then, the centroid of the triangle is