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If the pair of lines ax^2+2hxy+by^2=0,ax...

If the pair of lines `ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0` form a rhombus then prove that `(a-b)fg+h(f^2-g^2)=0`.

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The correct Answer is:
`(fg)/(h)`
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AAKASH SERIES-PAIR OF STRAIGHT LINES-SOLVED EXAMPLES
  1. Prove that the equation 6x^(2)+xy-12y^(2)-14x+47y-40=0 and 14x^(2)+xy^...

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  2. Show that product of the perpendicular distances from origin to pair o...

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  3. If the pair of lines ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0 form ...

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  4. The figure formed by the pairs of lines 3x^(2)+10xy+3y^(2)=0 and 3x^(2...

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  5. If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equi...

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  6. Let the equation ax^(2)+2hxy+2gx+2fy+c=0 represent a pair of parallel ...

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  7. IF the pair of lines represented by ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 int...

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  8. If two of the sides of a parallelogram are represented by ax^2+2hxy+by...

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  9. Find the equation to the pair of lines joining the origin to the point...

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  10. Show that the pair of lines joining the origin to the points of the in...

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  11. The chords of the curve 3x^(2)-y^(2)-2x+4y=0 subtend a right angle at ...

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  12. Find the equation of the pair of lines throughh the origin and forming...

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  13. Show that the lines x^(2)+16xy-11y^(2)=0 form an equilateral triangle ...

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  14. If (alpha, beta) is the centroid of the triangle, whose sides are ax^(...

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  15. The straight line lx+my+n=0 bisects and angle between the pair of line...

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  16. Two equal sides of an isoceles triangle are given by 7x-y+3=0 and x+y-...

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  17. Show that the product of the perpendicular from (alpha,beta) to the pa...

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  18. If the pair of lines ax^2+2hxy+by^2=0,ax^2+2hxy+by^2+2gx+2fy+c=0 form ...

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  19. If S=ax^(2)+2hxy+by^(2)+2gx+2fy+c=0 represents two straight lines equi...

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  20. Let the equation ax^(2)+2hxy+2gx+2fy+c=0 represent a pair of parallel ...

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