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How to calculate the pairs of starigh line from second degree curves

How to calculate the pairs of starigh line from second degree curves
 

Question Image
Grade:12th pass

1 Answers

Ram Kushwah
110 Points
5 months ago
 
The general equation of second degree can be written as:
    ax²+2hxy +by²+2gx+2fy+c=0.......(1)
This equation can represent a pair of straight lines if:
abc +2fgh-af²-bg²-ch²=0..............(2)
The given equation is:
2x²+5xy +3y²+6x+7y+4=0
So a=2,b=3,c=4,f=7/2,g=3 and h=5/2
Putting these values in LHS of eqn(2)
2 ×3 ×4 +  2 × (7/2) × (3)(5/2)  - 2 × (7/2)²- 3 × (3)²-4 × (5/2)²
=24+105/2 – 49/2 -27 -25
=24+(105-49)/2-52
= -28+(56/)/2
=-28+28
Thus we get
abc +2fgh-af²-bg²-ch²=0
Δ=0
Thus the given quadratic expression represents  one pair of straight lines

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