If $$2x+3y+4=0$$ is the perpendicular bisector of the line segment joining the points A(1, 2) and B($$\alpha,\beta$$), then the value of $$13\alpha+13\beta$$ equals

The equation of the pair of straight lines perpendicular to the pair $$2 x^2+3 x y+2 y^2+10 x+5 y=0$$ and passing though the origin is

If the centroid of the triangle formed by the lines $$2 y^2+5 x y-3 x^2=0$$ and $$x+y=k$$ is $$\left(\frac{1}{18}, \frac{11}{18}\right)$$, then the value of $$k$$ equals

If $$m_1$$ and $$m_2,\left(m_1>m_2\right)$$ are the slopes of the lines represented by $$5 x^2-8 x y+3 y^2=0$$, then $$m_1: m_2$$ equals