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The equation x 2 - 2 x y + y 2 + 3 x + 2  represents

Options

  1. AA parabola
  2. BAn ellipse
  3. CA hyperbola
  4. DA circle

Correct answer

A. A parabola

Step-by-step solution

Given equation is x 2 - 2 x y + y 2 + 3 x + 2 = 0 Comparing the above equation with a x 2 + 2 h x y + b y 2 + 2 g x + 2 f y + c = 0 Here, a = 1 ,   b = 1 ,   h = - 1 ,   g = 3 2 ,   f = 0 ,   c = 2 Now, Δ = a b c + 2 f g h - a f 2 - b g 2 - c h 2 ⇒ Δ = 1 1 2 + 2 0 3 2 - 1 - - 1 0 2 - 1 3 2 2 - 2 - 1 2 ⇒ Δ = - 9 4 i.e., Δ ≠ 0 and h 2 - a b = 1 - 1 = 0 i.e., h 2 = a b given equation represents a parabola

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