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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.

A

`(1)/(sqrt(2))` sq.units

B

`(1)/(sqrt(3))` sq.units

C

`(2)/(sqrt(3))` sq.units

D

`(sqrt(3))/(2)` sq.units

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The correct Answer is:
D
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NIKITA PUBLICATION-PAIR OF STRAIGHT LINES-MULTIPLE CHOICE QUESTIONS
  1. the area formed by the lines x^2-y^2=0 and x+8=0 is

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

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  3. Show that the lines x^2-4xy+y^2=0 and x+y=1 form an equilateral triang...

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  4. The coordinates of the orthocentre of the triangle formedby the lines ...

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  5. The area of the triangle formed by the lines 3x^(2)-4sqrt(2)xy+y^(2)=0...

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  6. If a + b = 2h, then the area of the triangle formed by the lines ax^2 ...

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  7. The length of each perpendicular side of an isoscele right angled tria...

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  8. Show that the straight lines x^2+4xy+y^2=0 and the line x-y=4 form a...

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  9. Show that straight lines (A^2-3b^2)x^2+8A Bx y(b^2-3A^2)y^2=0 form wit...

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  10. The area of triangle (in sq units) formed by the lines x^2- 4y^2 = 0 a...

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  11. If the area of the triangle formed by the pair of lines 8x^2 - 6xy + y...

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  12. The joint equation of pair of lines which bisects angle between the li...

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  13. The joint equation of bisectors of the angles between the lines given...

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  14. If the lines x^(2)+2hxy-y^(2)=0 bisect the angle between the lines 2x^...

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  15. If 7x^(2)-kxy-7y^(2)=0 represents the joint equation of the bisectors ...

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  16. The pair of lines h(x^(2)-y^(2))+pxy=0 bisects the angle between the p...

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  17. If the two pairs of line x^2 -2mxy -y^2=0 and x^2 - 2nxy -y^2 = 0 are ...

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  18. If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is a bisector of th...

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  19. The product of lenghts of the perpendicular from point (2, 3) on the l...

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  20. The product of legths of the perpendicular from point (4, 1) on the li...

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