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  • The angle between one of the lines given by  <img alt="\mathrm{a x^2+2 h x y+b y^2=0}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Ba%20x%5E2&plus;2%20h%20x%20y&am

The angle between one of the lines given by  \mathrm{a x^2+2 h x y+b y^2=0} , and one of the lines \mathrm{a x^2+2 h x y+b y^2+\lambda\left(\mathrm{x}^2+\mathrm{y}^2\right)=0} and the angle between the other two lines of the system are in the ratio \mathrm{k}: 1 where \mathrm{k}=

Option: 1

\frac{1}{2}


Option: 2

2


Option: 3

\frac{2}{5}


Option: 4

1


Answers (1)

best_answer

The equation of the bisectors of the angle between the lines \mathrm{a x^2+2 h x y+b y^2=0 \ldots \ldots \ldots (i) is \left(x^2-y^2\right) /(a-b)=x y / h}
and the equation of the bisectors of the angle between the lines \mathrm{\mathrm{a x^2+2 h x y+b y^2+\lambda\left(x^2+y^2\right)=0. or (a+\lambda) x^2+2 h x y+(b+\lambda) y^2=0}} is  \mathrm{\frac{x^2-y^2}{(a+\lambda)-(b+\lambda)}=\frac{x y}{h} \quad \Rightarrow\left(x^2-y^2\right) /(a-b)=x y / h. }

\mathrm{\therefore }Bisectors of angles between lines given by (i) and (ii) are the same. Hence the result.

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