The equation 4x^2 - 24xy + 11y^2 = 0 represen | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The given equation is a homogeneous equation of the second degree in $x$ and $y$ of the form $ax^2 + 2hxy + by^2 = 0$. Comparing $4x^2 - 24xy + 11

Vedclass · Accepted Answer

two lines through the origin

Vedclass · Answer

(C) The given equation is a homogeneous equation of the second degree in $x$ and $y$ of the form $ax^2 + 2hxy + by^2 = 0$. Comparing $4x^2 - 24xy + 11y^2 = 0$ with $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = -24$ (so $h = -12$),and $b = 11$. For a homogeneous equation of the second degree,the discriminant is $h^2 - ab = (-12)^2 - (4)(11) = 144 - 44 = 100$. Since $h^2 - ab > 0$,the equation represents two distinct real lines passing through the origin. Therefore,the correct option is $C$.

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

Similar Questions

The equation of the perpendiculars drawn from the origin to the lines represented by the equation $2x^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ is

The joint equation of lines passing through the origin and having slopes $(1+\sqrt{2})$ and $\frac{-1}{1+\sqrt{2}}$ is ...

The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0$. Then the value of $k$ is:

$A$ second degree homogeneous equation in $x$ and $y$ always represents:

The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :

Vedclass Test Series

Exam Paper Generator

Online Exam Module