Pair of Straight Lines

Q.

The three straight lines $\mathrm{ax}+\mathrm{by}=\mathrm{c},\mathrm{bx}+\mathrm{cy}=\mathrm{a}$ and $\mathrm{cx}+\mathrm{ay}=\mathrm{b}$ are collinear, if

1. $\mathrm{b}+\mathrm{c}=\mathrm{a}$

2. $\mathrm{c}+\mathrm{a}=\mathrm{b}$

3. $\mathrm{a}+\mathrm{b}+\mathrm{c}=0$

4. $\mathrm{a}+\mathrm{b}=\mathrm{c}$

Q. The conic represented by the equation $x^2+y^2-2xy+20x+10=0$ is

1. a hyperbola
2. a pair fo straight line
3. an ellipse
4. a parabola

Q.

If the equation
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
represents a pair of straight lines, then
$abc+2fgh-a{f}^2-b{g}^2+c{h}^2=0$

1. True

2. False

Q.

Which among the following equations represents a pair of straight lines?

1. x² - y² + x - y + 1 = 0

2. x² + 3xy + 2y² - x - 4y - 6 = 0

3. 3x² - 4xy - 7y² = 0

4. x² - 2x - y + 3 = 0

Q.

If the equation
$a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$
represents a pair of straight lines, then
$abc+2fgh-a{f}^2-b{g}^2+c{h}^2=0$

1. True

2. False