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If the equation ax^2+2hxy+by^2+2gx+2fy+c...

If the equation `ax^2+2hxy+by^2+2gx+2fy+c=0` represents a pair of lines, then show that the square of the distance of their point of intersection from the origin is `(c(a+b)-f^2-g^2)/(ab-h^2)`. Also show that the square of this distance is `(f^2+g^2)/(h^2+b^2)` if the given lines are perpendicular.

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AAKASH SERIES-PAIR OF STRAIGHT LINES-EXERCISE -5.2 LONG ANSWER QUESTIONS
  1. Prove that the equation 3x^(2)+7xy+2y^(2)+5x+5y+2=0 represents a pair ...

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  2. Find k, if the equation 2x^(2) + kxy - 6y^(2) + 3x + y + 1 = 0 represe...

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  3. The equation ax^(2) + 3xy - 2y^(2) - 5x +5y+c= 0 represents two lines ...

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  4. Find lambda in order that the equation x^(2)+lambda xy+y^(2)-5x=7y+6=0...

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  5. Show that the line x^2+2xy-35y^2-4x+44y-12=0" and "5x+2y-8=0 are conc...

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  6. Prove that the equations 6x^(2) + xy -12y^(2)–14x + 47y -40 = 0 and 14...

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  7. If the straight lines given by ax^(2) + 2hxy + by^(2) + 2gx + 2fy + c ...

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  8. Show that the following equations represents a pair of parallel lines ...

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  9. Show that the following equations represents a pair of parallel lines ...

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  10. Show that two pairs of lines 3x^(2)+8xy-3y^(2)=0 and 3x^(2)+8xy-3y^(2...

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  11. Show that the straight line y^2-4y+3=0" and "x^2+4xy+4y^2+5x+10y+4=0 f...

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  12. Show that two pairs of two straight lines 6x^(2)- 5xy – 6y^(2) = 0 and...

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  13. Find the product of lengths of perpendiculars drawn from (2, 1) upon t...

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

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  15. If the equation ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of lines,...

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  16. S.T the equation 2x^2-13xy-7y^2+x+23y-6=0 represents a pair of straigh...

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  17. Find the value of lambda for which the equation lambdax^(2) - 10xy + 1...

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  18. Show that the equation 8x^(2) - 24xy + 18y^(2)- 6x + 9y - 5 = 0 repres...

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  19. Show that the equation x^(2)-y^(2)-x+3y-2=0 represents a pair of perpe...

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