If the co-ordinate axes are the bisectors of the angles between the pair of lines $a x^2+2 h x y+b y^2=0$…

If the co-ordinate axes are the bisectors of the angles between the pair of lines $a x^2+2 h x y+b y^2=0$ where $h^2>a b$ and $a \neq b$, then
  1. $a+b=0$
  2. $h=0$
  3. $h \neq 0, a+b=0$
  4. $a+b \neq 0$

Solution

Equation of pair of bisectors of $ \begin{aligned} & a x^2+2 h x y+b y^2=0 \text { is } \frac{x^2-y^2}{a-b}=\frac{x y}{h} \\ & \text { if } \quad h=0, x y=0 \\ & \Rightarrow \quad x=0, y=0 \end{aligned} $ Which are the equations of coordinate axes

Asked in: AP EAMCET 2002

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