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Question

The ellipse x squared over z squared plus y squared over h squared equals 1 and the straight line y = mx + c intersect in real points only if

  1. a2m2 < c2 – b2    
  2. a2m2 > c2 – b2    
  3. a squared m squared greater or equal than c squared plus b squared   
  4. c greater or equal than b   

The correct answer is: a squared m squared greater or equal than c squared plus b squared 


    fraction numerator x to the power of 2 end exponent over denominator a to the power of 2 end exponent end fraction plus fraction numerator m to the power of 2 end exponent x to the power of 2 end exponent plus 2 m c x plus c to the power of 2 end exponent over denominator b to the power of 2 end exponent end fraction = 1
    Þ (b2 + a2 m2) x2 + 2 mca2 x + a2 (c2 - b2) = 0
    D > 0 Þ m2c2a4 - a2 (c2 - b2)(b2 + a2m2) > 0 Þ b2 + a2m2 > c2

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