Home
Class 12
MATHS
The equation x^(3)+x^(2)y-xy^(2)=y^(3) ...

The equation `x^(3)+x^(2)y-xy^(2)=y^(3)` represents

A

three real straight lines

B

lines in which two of them are perpendicular to each other

C

lines in which two of them are coincident

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
1 , 2 , 3
The equation is
`x^(2)(x+y)-y^(2)(x+y)=0`
or `(x+y)^(2)(x-y)=0`
It represents the lines `x+y=0,x+y=0,x-y=0`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Single)|23 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

  • PARABOLA

    CENGAGE|Exercise Question Bank|9 Videos

Similar Questions

Explore conceptually related problems

The equation x^(2)y^(2)-9y^(2)-6x^(2)y+54y=0 represents

The equation x^(2) - 2xy +y^(2) +3x +2 = 0 represents

Knowledge Check

  • If the equation kx^(2) – 2xy - y^(2)– 2x + 2y = 0 represents a pair of lines, then k =

    A
    2
    B
    -2
    C
    -5
    D
    3

  • The solution of the differential equation 2x (dy)/(dx)-y=3 represents

    A
    straight lines
    B
    circles
    C
    parabola
    D
    ellipse

    • Similar Questions

    Explore conceptually related problems

    Show that the equations 2x^(2)-xy-3y^(2)-6x+19y-20=0 represents a pair of intersecting lines. Show further that the angle between them is tan^(-1)(5) .

    Show that the equation 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lines. Find the distance between them.

    Show that the equation 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lines. Find the distance between them.

    Consider the equation (x^(3)+y^(3))dx-xy^(2)dy=0 i . Express this equation in the form (dy)/(dx)=(f(x,y))/(g(x,y))

    Show that the equation 2x^2-xy-3y^2-6x+19y-20=0 represents a pair of intersecting lines. Show further that the angle between them is tan^(-1) (5) .

    The equation, 2x^2+ 3y^2-8x-18y+35= K represents

    Home
    Profile