Home
Class 12
MATHS
Disuss the symmetry of x^(2)+xy+y^(2)=0....

Disuss the symmetry of `x^(2)+xy+y^(2)=0`.

Text Solution

Verified by Experts

If you substitute -x for or -y for y, but not both, the equation becomes `x^(2)-xy+y^(2)=0`, which does not preserve the equation. Therefore, the graph is not symmetrical with respect to either axis. However, if you substitute both -x for x and -y for y, the equation is preseved, so the equations is symmetric about the origin.
Promotional Banner

Topper's Solved these Questions

  • TRANSFORMATION AND SYMMETRY

    ENGLISH SAT|Exercise EXERCISES|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    ENGLISH SAT|Exercise EXERCISE|6 Videos

  • TRIANGLE TRIGONOMETRY

    ENGLISH SAT|Exercise EXERCISES|13 Videos

Similar Questions

Explore conceptually related problems

What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0 ?

What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0 ?

The asymptotes of the hyperbola 6x^(2) +13xy +6y^(2) -7x -8y-26 =0 are

The angle of rotation of axes to remove xy term in the equation x^(2) + 4xy + y^(2) - 2x + 2y -6=0 is

Find the asymptotes of the hyperola. 2x^(2)-xy-y^(2)+2x-2y+2=0

The equation of a hyperbola conjugate to the hyperbola x^(2)+3xy+2y^(2)+2x+3y=0 is

Subtract the sum of x^(2)-5xy +2y^(2) and y^(2)-2xy -3x^(2) from the sum of 6x^(2)-8xy-y^(2) and 2xy-2y^(2)-x^(2) .

y^2dx+(x^2-xy+y^2)dy=0

If 2x^(2)+5xy+2y^(2)-11x-7y+K=0 is the pair of asymptotes of the hyperbola 2x^(2)+5xy+2y^(2)-11x-7y-4=0 then K=

Disuss the continutiy of f(x) ={:{((sin^2 x)/(x^2)", "x ne 0),(" "0", " x= 0):}, at x=0