Condition for a Conic to Be a Pair of Straight Lines

Q. The value of k for which $2x^2+7\mathrm{xy}+3y^2+8x+14y+k=0$represents a pair of straight lines, is:

1. 2
2. 4
3. 8
4. 16

Q. The value of k for which the system of equations:
2x + 3y - 2z = 0; 2x - y + 3z = 0 and 7x + ky - z = 0 has non-trivial solution, is .

1. $k=-\frac{57}{5}$
2. $k=\frac{57}{5}$
3. $k=-\frac{57}{10}$
4. $k=\frac{57}{10}$

Q.

What is the condition for a conic $x^2+2xy+2y+kx+3y^2=0$ to represent a pair of straight lines.

1. $k=1$

2. $k=\frac{1}{2}$

3. $k=2$

4. $k=-\frac{1}{2}$