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  • The combined equation of the two lines and <img alt="a^{\prime} x+b^{\prime} y+c^

The combined equation of the two lines a x+b y+c=0 and a^{\prime} x+b^{\prime} y+c^{\prime}=0 can be written as (a x+b y+c)\left(a^{\prime} x+b^{\prime} y+c^{\prime}\right)=0.
The equation of the angle bisectors of the lines represented by the equation 2 x^2+x y-3 y^2=0 is

Option: 1

x^2-y^2-10 x y=0


Option: 2

x^2-y^2+10 x y=0


Option: 3

3 x^2+5 x y+2 y^2=0


Option: 4

3 x^2+x y-2 y^2=0


Answers (1)

best_answer

For pair of st. liens in form

a x^2+b y^2+2 h x y+2 g x+2 f y+c=0

equation of angle bisector is
$$ \begin{aligned} & \frac{x^2-y^2}{a-b}=\frac{x y}{h} \\ & \text { for } 2 \mathrm{x}^2+\mathrm{xy}-3 \mathrm{y}^2=0 \\ & \mathrm{a}=2, \mathrm{~b}=-3, \mathrm{~h}=\frac{1}{2} \end{aligned}
equation of angle bisector is
$$ \begin{aligned} & \frac{x^2-y^2}{5}=\frac{x y}{1 / 2} \\ & \Rightarrow \mathrm{x}^2-\mathrm{y}^2-10 \mathrm{xy}=0 \end{aligned}

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HARSH KANKARIA

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