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 ........
  1. \(h^2=a+b\)
  2. \(a+b=0\)
  3. \(h^2=a b\)
  4. \(h=0\)

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 \(\theta=90^{\circ}\) \(\Rightarrow \quad \tan \theta=\infty \quad \Rightarrow a+b=0\)

Asked in: AP EAMCET 2020 (17 Sep Shift 2)

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