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Find k, if the equation 2x^(2) + kxy - 6...

Find k, if the equation `2x^(2) + kxy - 6y^(2) + 3x + y + 1 = 0` represents a pair of lines. Find the point of intersection of the lines and angle between the lines for this value of k.

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Verified by Experts

The correct Answer is:
`k=4((-5)/(8),(-1)/(8)) cos^(-1)((1)/(sqrt(5))) (OR)`
`k=-((-5)/(7),(1)/(7)), cos^(-1)((4)/(sqrt(65)))`
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AAKASH SERIES-PAIR OF STRAIGHT LINES-EXERCISE - 4.2 ( LONG ANSWER QUESTIONS)
  1. S.T the equation 2x^2-13xy-7y^2+x+23y-6=0 represents a pair of straigh...

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  2. Prove that the equation 2x^(2)+3xy-2y^(2)+3x+y+1=0 represents a pair o...

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  3. Prove that the equation 2x^(2)+xy-6y^(2)+7y-2=0 represents a pair of s...

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

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  5. If x^(2)+xy-2y^(2)+4x-y+k=0 represents a pair of straight lines, find ...

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  6. Find lambda so that lambdax^(2)+5xy+4y^(2)+3x+2y+2=0 may represents a ...

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  7. Prove that the equation2x^(2)+3xy-2y^(2)-x+3y-1=0 represents a pair of...

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

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

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

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

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

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

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

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

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

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

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

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

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