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

Question

Ram Kushwah · Answer

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

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

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