Home
Class 12
MATHS
Show that the lines x^2-4xy+y^2=0 and x+...

Show that the lines `x^2-4xy+y^2=0 and x+y=1` form an equilateral triangle and find its area.

Text Solution

Verified by Experts

The correct Answer is:
`1/6sqrt(3) " ""squnit"`
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 3|9 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 4|10 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 1|9 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

Similar Questions

Explore conceptually related problems

Show that the straight lines x^2+4xy+y^2=0 and the line x-y=4 form an equilateral triangle .

Prove that the lines y=3x+1,y=4ndy=-3x+2 form an equilateral triangle.

Show that the lines x^(2) - 4xy + y^(2) = 0 and x + y = 10 contain the sides of an equilateral triangle.

Show that the straight lines represented by 3x^(2)+48xy+23y^(2)=0 and 3x-2y+13=0 form an equilateral triangle of area (13)/(sqrt(3)) sq.units.

If three lines 3x+4y=12," "5x+8y=40 and x axis form a triangle. Find its area

Show that the common tangents to the parabola y^(2)=4x and the circle x^(2)+y^(2)+2x=0 form an equilateral triangle.

Find the area of an equilateral triangle inscribed in the circle x^(2)+y^(2)-6x+2y-28=0

Find the equation of straight line which passes through the intersection of the straight line 3x+2y+4=0 and x-y-2=0 and forms a triangle with the axis whose area is 8 sq.unit

The equation of the in-circle of an equilateral triangle is x^(2)+y^(2)+2x-4y-8=0; find the area of the equilateral triangle.

Delta OAB is formed by the lines x^(2)-4xy+y^(2)=0 and the line AB.The equation of line AB is 2x+3y-1=0 .Find the equation of the median of the triangle drawn from the origin.