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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)))` .

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A DAS GUPTA-Pair of Straight Lines and Transformation of Axes-EXERCISE
  1. 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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  2. Prove that the bisectors of the between the lines ax^2+acxy+cy^2=0 and...

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  3. If the pairs of lines ax^2+2hxy+by^2=0 and a'x^2+2h'xy+b'y^2=0 have on...

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  4. Find the condition that the one of the lines given by ax^2+2hxy+by^2=0...

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  5. Show that the area of the triangle formed by the lines ax^2+2hxy+by^2=...

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  6. A pair of perpendicular straight lines is drawn through the origin ...

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  7. Show that the centroid (x',y') of the triangle with sides ax^2+2hxy+by...

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  8. If the lines ax^2+2hxy+by^2=0 be two sides of a parallelogram and the...

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  9. The straight lines represented by (y-m x)^2=a^2(1+m^2) and (y-n x)^2=a...

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  10. Find the combined equation of the straight lines passing through the p...

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  11. If the equation ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 resents a pair ...

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  12. If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about th...

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  13. The new equation of the curve 4(x-2y+1)^2+9(2x+y+2)^2 =25, if the lin...

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  14. The acute angle between the lines given by x^(2)+2(cosectheta)xy+y^(2)...

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  15. The difference of the slopes of the lines given by the equation x^2(se...

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  16. If the pair of straight lines x^2 - 2pxy - y^2 = 0 and x^2 - 2qxy -y^2...

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  17. The equation 12x^(2)+7xy-12y^(2)-18x+y+6=0 represents

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  18. The number of values of lambda for which the bisectors of the angle b...

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  19. If one of the lines of ax^(2)+2hxy+by^(2)=0 bisects the angle between ...

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  20. The equation (x+y+1)^2+k(x^2+y^2+1)=0 represents two straight lines th...

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  21. The equation 4x^(2)-24xy+11y^(2)=0 represents

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