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AP EAMCET202119 Aug 2021Evening ShiftMathematicsPair of LinesActual

If the acute angle between lines a x 2 + 2 h x y + b y 2 = 0 is π 4 , then 4 h 2 =

Options

  1. Aa 2 + 4 a b + b 2
  2. Ba 2 + 6 a b + b 2
  3. C( a − 2 b ) ( 2 a + b )
  4. Da 2 − 6 a b + b 2

Correct answer

B. a 2 + 6 a b + b 2

Step-by-step solution

We know that, the angle between lines of a homogenous pair is θ = tan - 1 2 h 2 - a b a + b     ⇒ π 4 = tan - 1 2 h 2 - a b a + b   ⇒   tan   π 4 = 2 h 2 - a b a + b ⇒ 2 h 2 - a b a + b = 1   ⇒ 4 h 2 - a b = a + b 2   ⇒   4 h 2 = a 2 + b 2 + 6 a b

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