Q45 / 160 · WBJEE 2011 · Mathematics

The equation \(8 x^2+12 y^2-4 x+4 y-1=0\) represents

  • Correct answer
    A
    an ellipse
  • B
    a hyperbola
  • C
    a parabola
  • D
    a circle

Solution

Hints: \(a x^2+b y^2+2 h x y+2 g x+2 f y+c=0\) represents ellipse if \(\mathrm{h}^2-a b < 0\) \(\begin{aligned} & 3 x^2+12 y^2-4 x+4 y-1=0 \\ & h=0, a=3, b=12 \\ & h^2-a b < 0 \end{aligned}\)

Hence, the correct answer is option: 'A'.

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