Question

The equation $4x^2-24xy+11y^2=0$represents

• A. Two parallel lines
• B. Two perpendicular lines
• C. Two lines through the origin
• D. A circle

Answer 1

The correct option is C

Two lines through the origin

Explanation for the correct option

Given, $4x^2-24xy+11y^2=0$

On comparing the above equation with the standard form $a{x}^2+2hxy+b{y}^2=0$ we get,

$a=4,h=-12,b=11$

Now, $h^2-ab=144-44=100>0$

Since the equation $4x^2-24xy+11y^2=0$is a homogeneous equation and $h^2-ab>0$,the given equation represents two lines passing through the origin.

Hence, Option(C) is the correct answer.