Straight Lines — JEE Main PYQs

If the pair of lines $a{x}^2+2(a+b)xy+b{y}^2=0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then

Let $\mathrm{A}(2,-3)$ and $\mathrm{B}(-2,1)$ be vertices of a triangle ABC. If the centroid of this triangle moves on the line $2x+3y=1$, then the locus of the vertex C is the line

The equation of the straight line passing through the point $(4,3)$ and making intercepts on the co-ordinate axes whose sum is -1 is

If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product, then c has the value

If one of the lines given by $6x^2-xy+4c{y}^2=0$ is $3x+4y=0$, then $c$ equals