The lines represented by \(a x^2+2 h x y+b y^2=0\) are perpendicular to each other, if ........
The lines represented by \(a x^2+2 h x y+b y^2=0\) are perpendicular to each other, if ........
\(h^2=a+b\)
\(a+b=0\)
\(h^2=a b\)
\(h=0\)
Solution
Pair of straight lines through origin are given by
\(a x^2+2 h x y+b y^2=0\)
Angle " \(\theta\) ' between lines is given by,
\(\tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|\)
When lines are perpendicular \(\theta=90^{\circ}\)
\(\Rightarrow \quad \tan \theta=\infty \quad \Rightarrow a+b=0\)