The equation $3 x^{2} - 2 x y + y^{2} = 0$ represents:

a circle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

hyperbola

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a pair of lines

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is C none of these
Given expression, $3 x^{2} - 2 x y + y^{2} = 0$
As Coefficient of $x y$ is not zero,It will not be a circle and hyperbola.
Let $\frac{y}{x} = m$
We get $m^{2} - 2 m + 3 = 0$ will not have any real solutions as discriminant is less than zero.
$∴$ They will not be pair of lines too.

Suggest Corrections

Similar questions

If the pairs of lines $x^{2} + 2 x y + a y^{2} = 0$ and $a x^{2} + 2 x y + y^{2} = 0$ have exactly one line in common then the joint equation of the other two lines is given by

Q. If the pairs of lines

x^{2} + 2 x y + a y^{2} = 0

and

a x^{2} + 2 x y + y^{2} = 0

have exactly one line in common, then the combined equation of the other two lines is given by

Q. The angle between the pair of lines given by equation

x^{2} + 2 x y - y^{2} = 0

is:

Q. If the pair of lines

x^{2} + 2 x y + a y^{2} = 0

and

a x^{2} + 2 x y + y^{2} = 0

have exactly one line in common, then prove that joint equation of the other two lines is given by

3 x^{2} + 10 x y + 3 y^{2} = 0

Find the equation of the bisectors of the angle between the lines represented by $3 x^{2} - 5 x y + 4 y^{2} = 0$

Join BYJU'S Learning Program

The equation 3x2−2xy+y2=0 represents:

The correct option is C none of theseGiven expression,3x2−2xy+y2=0 As Coefficient of xy is not zero,It will not be a circle and hyperbola.Let yx=mWe get m2−2m+3=0 will not have any real solutions as discriminant is less than zero.∴ They will not be pair of lines too.

The equation $3 x^{2} - 2 x y + y^{2} = 0$ represents: