Question

The condition that the two lines represented by the equation $a{x}^2+2hxy+b{y}^2=0$ to be perpendicular are

• A. $ab=-1$
• B. $a=-b$
• C. $a=b$
• D. $ab=1$

Answer 1

The correct option is B

$a=-b$

Explanation for the correct option:

Find the condition :

Given the equation is $a{x}^2+2hxy+b{y}^2=0$

We know that the angle between the two lines $a{x}^2+2hxy+b{y}^2=0$given by

$\tan \left(\theta \right)=\frac{2\sqrt{h^2-ab}}{a+b}$

Given lines are perpendicular. so $\theta ={90}^0$

$\begin{array}{rcl}& \Rightarrow & \tan \left({90}^0\right)=\frac{2\sqrt{h^2-ab}}{a+b}\\ & \Rightarrow & \infty =\frac{2\sqrt{h^2-ab}}{a+b}\\ & \Rightarrow & a+b=0\\ & \Rightarrow & a=-b\end{array}$

Hence, the correct option is (B).