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If \mathrm{(a+b)^2=4 h^2}, then one of the lines given by the equation \mathrm{ a x^2+2 h x y+b y^2=0}  will divide the angle between the coordinate axes in the ratio \mathrm{ \mathrm{k}: 1}, where \mathrm{ \mathrm{k}=}

Option: 1

1


Option: 2

2


Option: 3

\frac{1}{3}


Option: 4

\frac{1}{2}


Answers (1)

best_answer

The equation of the bisectors of the angles between the coordinate axes are  \mathrm{y=x}  and  \mathrm{y=-x}  If  \mathrm{y=x}  is one of the lines given by  \mathrm{a x^2+2 h x y+b y^2=0}  then substitution  \mathrm{y=x}  in (i), we get\mathrm{ a+b=2 h}\mathrm{ a+b=2 h}  and if  \mathrm{ y=-x}  is one of the lines given by (i), then we get  

\mathrm{ a+b=-2 h \therefore} One of the lines given by (i) bisects the angle between the coordinate axes if  \mathrm{ a+b= \pm 2 h} squaring, we have  \mathrm{ (a+b)^2=4 h^2}.

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