Question

$a{x}^2+2hxy+b{y}^2=0$ always represents a pair of straight lines passing through the origin. If
$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{a.}{h}^2>ab& \text{1. Lines are coincident}\\ \text{b.}{h}^2=ab& \text{2. Lines are real and distinct}\\ \text{c.}{h}^2<ab\text{3. Lines are imaginary with real point of intersection i.e. (0,0)}& \end{array}$

• A. a-1 b-2 c-3
• B. a-2 b-1 c-3
• C. a-3 b-2 c-1
• D. a-3 b-1 c-2

Answer 1

The correct option is B

a-2 b-1 c-3

A Homogeneous equation of degree two is $a{x}^2+2hxy+b{y}^2=0$ represents pair of straight lines passing through the origin.

Condition for pair of straight lines passing through origin.

1.If $h^2$> ab

Lines are distinct and real

2.When $h^2$ = ab

Both the lines are coincident

3.When $h^2$ < ab

Lines are imaginary with real point of intersection i.e. (0,0)