Find the lines whose combined equation is `6x^2+5x y-4y^2+7x+13 y-3=0`

1.	Find the lines whose combined equation is `6x^2+5x y-4y^2+7x+13 y-3=0`
Answer» The given equation of pair of straight lines is `6x^(2)+5xy-4y^(2)+7x+13y-3=0` or `6x^(2)+(5y+7)x-(4y^(2)-13y+3)=0` Solving it as a quadratic in x,we get `x=((5y+7)+-sqrt((5y+7)^(2)+24(4y^(2)-13y+3)))/(12)` `=(-(5y+7)+-sqrt(121y^(2)-242y+121))/(12)` `=(-(5y+7)+-11(y-1))/(12)` `=(6y-18)/(12),(16y+4)/(12)or(y-3)/(2),(-4y+1)/(3)` The two straight lines are `2x-y++3=0and3x+4y-1=0`.

Discussion

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