IPMAT Indore (SA) PYQs

Let $A(1,3)$ and $B(5,1)$ be two points. If a line with slope $m$ intersects $AB$ at an angle of $45°$, then the possible values of $m$ are

The equation of the straight line passing through the point $M (-5,4)$, such that the portion of it between the axes is divided by the point $M$ into two equal halves, is

If one of the lines given by the equation $2x^2 + axy + 3y^2 = 0$ coincides with one of those given by $2x^2 + bxy - 3y^2 = 0$ and the other lines represented by them are perpendicular then $a^2+b^2 =$