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If the pairs of straight lines `ax^2+2hxy-ay^2=0 and bx^2+2gxy-by^2=0` be such that each bisects the angles between the other , then prove that hg+abd=0.

A

one pair bisects the angle between the other pair

B

the lines of one pair are equally inclined to the lines of the other pair

C

the lines of each pair are perpendicular to other pair

D

all of these

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-PAIR OF STRAIGHT LINES-Chapter Test
  1. If the lines given by ax^(2)+2hxy+by^(2)=0 are equally inclined to the...

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  2. The equation to the striaght lines passing through the origin and maki...

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  3. Prove that the limiting points of the system x^(2)+y^(2)+2gx+c+lamda(x...

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

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  5. The equation to the pair of straight lines bisecting the angles betwe...

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  6. If the pair of lines sqrt(3)x^2-4x y+sqrt(3)y^2=0 is rotated about the...

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  7. Show that if two of the lines ax^3+bx^2y+cxy^2+dy^3=0 (a ne 0) make co...

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  8. If the pairs of straight lines ax^2+2hxy-ay^2=0 and bx^2+2gxy-by^2=0 b...

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  9. The equation a^2x^2+2h(a+b)x y+b^2y^2=0 and a x^2+2h x y+b y^2=0 repre...

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  10. If (x^(2))/(a) + (y^(2))/(b) + (2xy)/(h) =0 represent pair of straig...

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  11. If the lines represented by the equation ax^(2)+2hxy+by^(2)+2gx+2fy+c=...

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  12. The distance between the two lines represented by the  sides of an equ...

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  13. The equation of the image of the lines y=|x| in the line mirror x = 2 ...

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  14. If the equation 3x^(2)+xy-y^(2)-3x+6y+k=0 represents a pair of straigh...

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  15. The equation of second degree x^2+2sqrt2xy+2y^2+4x+4sqrt2y+1=0 represe...

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  16. The value of lambda for which the equation x^2-y^2 - x - lambda y - ...

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  17. Distance between the pair of lines represented by the equation x^(2)-6...

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  18. The equation x^2 - 3xy+ lambday^2 + 3x - 5y + 2 = 0 where lambda is a ...

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