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Show that straight lines (A^2-3b^2)x^2+8...

Show that straight lines `(A^2-3b^2)x^2+8A Bx y(b^2-3A^2)y^2=0` form with the line `A x+B y+C=0` an equilateral triangle of area `(C^2)/(sqrt(3(A^2+B^2)))` .

A

`sqrt(3)`

B

`2sqrt(3)`

C

`3`

D

`12`

Text Solution

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The correct Answer is:
A
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NIKITA PUBLICATION-PAIR OF STRAIGHT LINES-MULTIPLE CHOICE QUESTIONS
  1. The length of each perpendicular side of an isoscele right angled tria...

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

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

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

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

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

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

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

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

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

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

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

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

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  15. The equation of the bisectors of angle between the lines x^(2)-4xy+y^(...

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  16. DeltaOAB is formed by the lines x^2-4xy +y^2= 0 and the line AB. The e...

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  17. 9.y If two sides of a triangle are represented by x^27xy+6y^2=0 and th...

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  18. Orthocentre of the triangle formed by the lines xy=0 and x+y=1 is

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  19. Orthocentre of the triangle formed by the lines 3x^(2)+8xy-y^(2)=0 and...

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  20. The angle between the lines xd^(2)+4xy+y^(2)=0 is

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