Homogenization

Q. If the lines represented by $a{x}^2+8xy+3y^2=0$ are mutually perpendicular, then

1. $x-3y=0$ is one of the line representing pair of lines
2. $|a|=3$
3. $y-3x=0$ is one of the line representing pair of lines
4. $|a|=\frac{8}{3}$

Q.

The lines joining the points of intersection of line x + y = 1 and curve $x^2+y^2-2y+\lambda =0$ to the origin are perpendicular, then the value of $\lambda$ will be

1. 1/2

2. 0

3. -1/2

4. 

Q.

The equation of pair of straight lines joining the point of intersection of the curve $x^2+y^2=4$ and y - x = 2 to the origin, is

1. 

2. 

3. 

4.