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BITSAT2012MathematicsHyperbolaActual

Find the eccentricity of the conic represented by x²-y²-4 x+4 y+16=0

Options

  1. A2
  2. B2
  3. C2 2
  4. D3 2

Correct answer

B. 2

Step-by-step solution

We have x²-y²-4 x+4 y+16=0 (x²-4 x )- (y²-4 y )=16 (x²-4 x+4 )- (y²-4 y+4 )=-16 (x-2)²-(y-2)²=-16 (x-2)² 4² - (y-2)² 4² =1 This is rectangular hyperbola, whose eccentricity is always 2 .

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