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Find the value of k so that the equation of pair of line x 2 +kxy+2y 2 +3x+5y+2=0

Find the value of k so that the equation of pair of line x2+kxy+2y2+3x+5y+2=0

Grade:11

1 Answers

Harsh Tiwari
54 Points
2 years ago
the condition for a general quadratic equation of the form ax^2+by^2+2gx+2fy+2hxy+c=0 to represent a pair of straight lines (POSL) is that the determinant should be 0.
Here,
a=1, b= 2, g= 3/2, f= 5/2, h= k/2, c=2
so we form the determinant as follows:
|  1       k/2    3/2|
| k/2      2      5/2| = 0
| 3/2    5/2       2 |
putting this determinant 0, we get
 K= 3, 9/2

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