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The slope of one of the straight lines `ax^(2)+2hxy+by^(2)=0` is twice that of the other, show that `8h^(2)=9ab`.

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SURA PUBLICATION-TWO DIMENSIONAL ANALYTICAL GEOMETRY-EXERCISE 6.4
  1. Find the combined equation of the straight lines whose separate equati...

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  2. Show that 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lin...

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  3. Show that 2x^(2)+3xy-2y^(2)+3x+y+1=0 represents a pair of perpendicula...

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  4. Show that the equations 2x^(2)-xy-3y^(2)-6x+19y-20=0 represents a pair...

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  5. Prove that the equations to the straight lines through the origin each...

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  6. Find the equation of the pair of straight lines passing through the po...

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  7. Find the separate equation of the following pair of straight lines 3...

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  8. Find the separate equation of the following pair of straight lines 6...

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  9. Find the separate equation of the following pair of straight lines 2...

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  10. The slope of one of the straight lines ax^(2)+2hxy+by^(2)=0 is twice t...

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  11. The slope of one of the straight lines ax^(2)+2hxy+by^(2)=0 is three t...

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  12. A DeltaOPQ is formed by the pair of straight lines x^(2)-4xy+y^(2)=0 a...

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  13. Find p and q, if the following equation represents a pair of perpendi...

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  14. Find the value of k if the following equation represents a pair of str...

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  15. For what value of k does the equation 12x^(2)+2kxy+2y^(2)+11x-5y+2=0 r...

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  16. Show that the equation 9x^(2)-24xy+16y^(2)-12x+16y-12=0 represents a p...

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  17. Show that the equation 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of...

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  18. Prove that one of the straight lines given by ax^(2)+2hxy+by^(2)=0 wil...

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  19. Prove that the straight lines joining the origin to the points of inte...

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