Question

Equation $6x^2-5xy+y^2=0$ represents____________________

• A. Pair of coincident lines
• B. Pair of imaginary lines with real point of intersection i.e.(0,0)
• C. Pair of distinct straight lines
• D. None of these

Answer 1

The correct option is C

Pair of distinct straight lines

Given equation is a homogeneous equation of second degree so, it represents a pair of straight line passing through origin.

Comparing the equation with $a{x}^2+2hxy+b{y}^2=0$

We obtain a=6, b=1, h= $-\frac{5}{2}$

$h^2-ab=\frac{25}{4}-6=\frac{1}{4}$

$h^2-ab>0\Rightarrow h^2>ab$

$h^2>ab$

Hence, given equation represents a pair of distinct straight lines passing through the origin.

Option C is correct.